The answer to this question depends on your viewpoint. For example, as an archeological discovery, the excavation of Noah's Ark would be very important. The existence of the remains of a giant boat, which could be carbon-dated to 2500 BC, the time indicated by the Bible for the great flood, and which showed evidence that it had once carried different species of animals, would be a fascinating historical find. It would also be important to Bible-believing Christians, as it would confirm and support the biblical account. For skeptics and people who are unsure whether to trust the Bible, it could also be important in the sense that it might remove doubt. But for those who are unwilling to believe in the Bible, the discovery of Noah's Ark would probably not be very important.
How important would the discovery of Noah's Ark be?
Ultimately, faith is not dependent upon scientific, archeological, or historical evidence. While discoveries which support the biblical record are met with joy and awe by Christians, they are regarded with an equal amount of distrust by skeptics. Ultimately, belief in God comes from a heart that loves God. If Noah's Ark is never found, Christians will not lose that love for Him. If it is found, it will not create love for Him in the heart of an atheist. It is likely that if Noah's Ark is found, Christians will find it important, but atheists will present alternate explanations for the existence of the Ark, theorizing that it can't really be the boat that Noah built.
This strange dichotomy is not so very strange when we consider the words of Paul, who pointed out that people know that God exists. Nature makes it plain to them that there is a divine Creator, through the things that have been made. But they reject the obvious, not because they don't see it, but because they desperately want to believe that He does not exist (Romans 1:19–20). His existence would necessitate the acceptance of the truth—that we are all fallen and need a Savior (Romans 3:23; 1 John 1:8–10). Jesus also stated that a man who does not have the love of God in his heart will not accept the truth, even if someone returns from the dead and tells them that God and Heaven and Hell are real (Luke 16:31).
This being the case, the discovery of Noah's Ark will probably not convince anyone who is not already predisposed to being convinced. But for Christians, and those who do want to see the Bible supported, it would be an amazing and fascinating discovery.
Questions about Noah's ark: How long did it take Noah to build the ark? How long was Noah on the ark?
Was the Noahic flood global?
Is creationism scientific?
Creation vs. evolution - What does the Bible say?
Faith vs. science. Is there a contradiction between faith in God and science?
Truth about Creation