Perhaps. If the de facto president were ruled ineligible, that would mean a President had never qualified. Under the 12th and 20th amendments, the Vice President is to act as President until a President shall have quallified. Then the House would need to select a President from the 2 highest Presidential electoral vote recipients. That woudl be McCain. Then we'd have to go 'round the circle again to determine if McCain was eligible, as there would be certain to be challenges to that.
Why? The Electoral College votes on both president and vice-president. Even if Obama was found to be ineligible that doesn't mean Biden was.