It is not actually legal to do this. A state can't interfere with the functioning of the federal executive branch. Most constitutional scholars would say the sentence just gets suspended until the end of his term.
It wouldn't effect the functioning of the federal system. You seem to forget he spent the majority of his time in his idiotic faux gold penthouse or at Mar a lago.
Dumping him into white collar prison wouldn't change any of that and fed prisoners can still get temporary hardship/work release anyway.