If Obama 'fails to qualify' then he's not going to be a figurehead, he's going back to the Senate (at least at first). Joe Biden will be President, for all intents and purposes.
It's not like Obama would qualify at a later time. There'd be no reason for Biden, who's wanted to be President for decades, to play puppet for a former rival who will go from Messiah to pariah in a single news cycle. If Obama is caught intentionally falsifying paperwork to become president, a large chunk of Democrats will turn on him, as well as all independents and Republicans.
There's about 20% of the electorate which would be happy if Obama made diapers out of the Constitution, and filled them while he was inaugurated. They'll scream bloody murder if a Constitutional challenge is raised, regardless of how fair or legal it is.
I can see it now... “it’s just sex” becomes “its just birth”