Not if Obama is immediately jailed and replaced for being unable to Constitutionally carry out his duties. He’s actually never been able to Constitutionally carry out his duties because of the 20th Amendment, but if he was in jail there would be no denying that he is unable to do so.
Of course, Joe Biden would probably just pardon them both...
The problem with your idea is this: Just who the hell do we have in DC that has the Constitutional Fortitude and BALLS to take Ubama into custody?
Boehner?
McConnell?
Who?