No. You could produce video proof of his birth in a Kenyan sh*t-hole and no court will overturn the election.
It's not a matter of "overturning the election". This is not a dispute about counting votes, casting votes, or even eligibility to vote. It's about enforcing the provision of the Constitution that provided that only a natural born citizen is eligible to the office of President. The resolution will not involve any new elections...unless the court also declares that the electors where fraudulently elected. But I don't expect that, at not with the cases now in the courts, because AFAIK, that is not at issue.