“Can a person be saved by Christ if all they have is natural/general revelation and not the gospel?”
First, definitions are in order. Inclusivism is the belief that general revelation (nature; the conscience of man) is sufficient to save, as God might judge man righteous based on what little faith they may have, despite that faith not being in Jesus Christ; those of other religions may very well be saved. Exclusivism is the belief that people must come into contact with the saving knowledge of the gospel to be saved. Not only does general revelation not contain the knowledge of salvation, but in their sinful state, man suppresses what knowledge they do have in general revelation. A further definition of general and special revelation will help to frame the contents of this discussion:
General revelation is rooted in creation and in the general relations of God to man, is addressed to man considered simply as the creature and image-bearer of God, and aims at the realization of the end for which man was created and which can be attained only where man knows God and enjoys communion with him. Special revelation, on the other hand, is rooted in the redemptive work of God, is addressed to man as a sinner and adapted to the moral and spiritual needs of fallen man, and aims at leading the sinner back to God through the specific knowledge of God’s redemptive love revealed in Christ Jesus. It is not like general revelation a light that lighteth every man, but a light that illumines the pathway of those who are made receptive for the truth by the special operation of the Holy Spirit. 
I believe the answer to the above question is rather simple, as it is explicitly taught in Scripture. The answer, simply put, is no, a person cannot be saved apart from a knowledge of the gospel. In other words, exclusivism is true. Yet, it troubles me how often I have come across (Evangelical) Christians who respond with a YES. In this post, I hope to defend the exclusive characteristic of the gospel — people must have a knowledge of Christ as revealed in the gospel and believe in this gospel if they are to be saved. The following consists of a brief look at Psalm 19 and Romans 1:18-20 as supporting the exclusivist position, followed by a brief look at additional arguments.
General revelation in verses 1-6. There are at least four essential things that need to be taken note of in this passage. First, we do find that something of the glory of God is communicated to mankind by means of this general revelation: “The heavens declare the glory of God, and the sky above proclaims his handiwork” (v. 1). However, we are not told what exactly this knowledge consists of. Second, this is a non-verbal revelation, and only so much can be communicated non-verbally. Third, notice that David (the psalmist) uses “God” in this passage. This word is not unique to the one true God and can be used to refer to the gods of the nations. Fourth, there are no spiritual blessings mentioned in this passage.
Special revelation in verses 7-14. Again, there are at least four essential things to notice in this passage. First, we are now dealing with verbal revelation (the law of God). More knowledge can be communicated verbally than non-verbally. Second, David does not use “God” in this passage, but he uses “LORD” (i.e. Yahweh), the covenant name of God. This name is unique to the one true God, the God of Abraham, Isaac, and Jacob. Third, spiritual blessings are mentioned in this passage as the result of this special revelation (i.e. “reviving the soul;” “making wise the simple;” “rejoicing the heart;” “enlightening the eyes”). Finally, in verse 14, the LORD is specifically referred to as the Redeemer.
Paul’s focus is on general revelation (v. 20). Now, what does Paul say this general revelation reveals? The wrath of God. Now, I think it’s rather obvious that general revelation does not inherently reveal the wrath of God. In other words, there’s nothing inherent in the nature of general revelation that necessitates it revealing God’s wrath. Rather, the wrath of God is revealed from heaven because sinful mankind suppresses, by their unrighteousness, what truth they know of God through creation. In other words, mankind instinctively knows that God exists and that he is the Creator of all things. However, they live in continual disobedience to him, choosing to believe a lie (v. 25). Additionally, the results of the curse are exhibited in creation through various “natural disasters”. Such events further testify to God’s wrath over sinful mankind. Mankind knows, instinctively, that they are worthy of God’s judgment. It’s as if nature testifies against them! Again, the knowledge of God revealed in nature is minimal: “For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse” (v. 20). While man may garner some understanding of what God is like by observing nature (just think of the ancient Greek philosophers), such knowledge is minimal and open to all sorts of twisting within man’s religions (again, just think of the ancient Greek philosophers). What little knowledge of God is revealed in creation is suppressed by fallen mankind by their sinful and rebellious acts.
Notice also that there are no salvific blessings mentioned with regard to general revelation, which is the same thing we saw in Psalm 19:1-6. But this is Paul’s point. Remember what Paul just stated before this passage: “For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. For in it the righteousness of God is revealed from faith for faith, as it is written, ‘The righteous shall live by faith’” (vv. 16-17). So after introducing the salvific nature of the gospel (special revelation), Paul discusses the non-salvific nature of creation (general revelation). Keep in mind that 1:16-17 is Paul’s thesis of his letter. Romans is essentially an apologetic for missions (preaching the gospel among the nations, especially to those who have yet to hear; cf. Rom. 10:14-17; 15:23-24). In short, Paul is making the case that mankind is hopeless apart from the saving knowledge of the gospel. This is the means that God uses to save his people (1 Thess. 1:4-5; 2 Thess. 2:13-14; 2 Tim. 2:10).
Further Arguments for Exclusivism
General revelation is insufficient to save, first and foremost, because it is rooted in or founded from the very beginning (of creation), prior to the need of redemption. This may very well be one of the most overlooked characteristics of general revelation by inclusivists. Some within the inclusivist perspective have questioned, in an attempt at ridiculing the exclusivists, “What kind of God would reveal enough knowledge of himself to condemn mankind, but not to save it?” At first glance, such a question may seem to have some merit. However, there is a fundamental flaw in the question. It assumes that general revelation was given sometime after the Fall of man. This, of course, is not the case. What is revealed in general revelation today is what was revealed in general revelation from the moment of creation (to say nothing of the results of the curse within creation); and, of course, there was no need of redemption when God created. Indeed, he made all things very good (Gen. 1:31). It’s not until Genesis 3 that Adam sins and so casts all of humanity after him into spiritual ruin. Now special revelation is necessary (e.g. Gen. 3:15, 21), for special revelation communicates that knowledge of salvation not present within general revelation. It was never God’s intention that general revelation communicate knowledge unto salvation.
According to Scripture, mankind is evil, corrupt, wicked, darkened, hard-hearted, by nature children of wrath, etc. (e.g. Gen. 6:5, 11-12; Jer. 17:9; Mk. 7:20-23; Eph. 2:1-3; 4:17-19). What fallen, sinful mankind needs is a radical, powerful transformation; they need to be born again (Jn. 3:3-5). Yet, it is not in the power of general revelation, as glorious as it may be, to do such a thing. Rather, the gospel is the power of God unto salvation (Rom. 1:16-17). Further, the Holy Spirit works through the proclamation of the gospel to bring about regeneration, repentance, and faith (e.g. 1 Thess. 1:4-5; 2 Thess. 2:13-14); but this cannot be said with regard to general revelation. In short, general revelation does not communicate the saving knowledge of the gospel, and therefore does not have the power to save.
The Scriptures specifically teach that men and women must come into contact with the gospel if they are to believe and be saved. Perhaps one of the most striking passages on this is Romans 10:13-17. The text is rather straight-forward. People must call on the name of the Lord in faith if they are to be saved. But Paul then notes what must logically take place for this to happen: People can’t call on the Lord if they haven’t believed in him; they can’t believe in him if they haven’t heard of him; they can’t hear without a preacher; and a preacher can’t preach unless he is sent. Then comes the capstone of the text, “So faith comes from hearing, and hearing through the word of Christ [the gospel]” (v. 17). In short, people must come into contact with the gospel if they are to be saved. This completely undercuts any notion that those of other religions can and may be saved while still within those religions. Note these other passages:
1 John 1:1-4 “That which was from the beginning, which we have heard, which we have seen with our eyes, which we looked upon and have touched with our hands, concerning the word of life—the life was made manifest, and we have seen it, and testify to it and proclaim to you the eternal life, which was with the Father and was made manifest to us— that which we have seen and heard we proclaim also to you, so that you too may have fellowship with us; and indeed our fellowship is with the Father and with his Son Jesus Christ. And we are writing these things so that our joy may be complete.” (Emphasis added.)
2 Timothy 2:8-10 “Remember Jesus Christ, risen from the dead, the offspring of David, as preached in my gospel, for which I am suffering, bound with chains as a criminal. But the word of God is not bound! Therefore I endure everything for the sake of the elect, that they also may obtain the salvation that is in Christ Jesus with eternal glory.” (Emphasis added.)
Before drawing to a close, let me briefly respond to what seems to be a common question posed by inclusivists. I have heard and seen it asked (in various ways), “What about Old Testament saints? If people have to come in contact with the gospel to be saved, then how were they saved?” Simple, they were likewise saved by the gospel. Let us not forget that the Israelites were God’s specially chosen people from among the nations. They were surrounded by special revelation (e.g. prophets; the tabernacle along with its sacrifices). Their revelation of the gospel certainly wasn’t as full as it has been since the first advent of Jesus Christ, but that doesn’t mean they didn’t have the gospel. In fact, Paul explicitly tells us that they were saved in the same way (Rom. 3:19-26; note especially v. 26; cf. Gal. 3:8). Whereas they looked forward to the promises of God as revealed by the prophets and the tabernacle sacrifices (etc.), we look back to the finished work of Christ recorded for us in the New Testament.
I believe a fundamental problem that leads to the inclusivist position is the denial of God’s sovereignty in salvation. If you believe God is eagerly seeking the salvation of those who never hear the gospel, rather than concluding that God has failed, you must find a way to broaden the way of salvation (contra Mtt. 7:13-14). Additionally, many within the inclusivist perspective speak as if God owes salvation, or at least a “chance” at it, to mankind, as if God would be unjust not to make it universally accessible. Such, of course, goes against the very concept of grace. Grace cannot be merited or demanded, otherwise it is no longer grace. Further, those within the inclusivist perspective typically have a less-than-biblical view of mankind. They typically believe man to be better than he is actually presented in the Bible. I get the sense that many inclusivists view mankind as victims in the world, rather than suspects in the court of God. People think that mankind deserves salvation, but we don’t. That’s what’s so amazing about it, that God would choose to save any (amazing grace!). Finally, I believe many inclusivists have an unbalanced view of God’s character, often focusing on his love to the exclusion or minimization of his other attributes (e.g. holy; just).
 Berkhof, Louis. Manual of Christian Doctrine (MI: Eerdmans Publishing Co., reprinted 2002), 25.