Maybe. It would fit Obama’s psyche. It would make him 100% eligible though.
Eligibility has been resolved anyway. We've now had approximately 57 presidential elections and in each of those elections, the qualifications of the presidential candidates has been determined by the voters and their electors. The Constitution empowers the voters and their electors to select our presidents (without any candidate approval or screening by the Supreme Court). The Supreme Court will never dare try to sneak its nose under that tent to try to disqualify a candidate. In America, the people are the masters and the Supreme Court their servant.