The biggest impact would be that we would have found new tools and discovered new properties. Currently the only tools we have when dealing with infinite set is Cantor's diagonal argument, Godel's first incompleteness theorem, halting problem all based on the diagonal argument. However, when tring to prove P and NP, diagonal argument doesn't apply, and that is why it is so difficult. Even proofing P = NP? is undecidable still sheds light of the structure of these classes of problems.