I don't know, as cool as this is, wouldn't he not be selected mostly because well, I've heard when Letterman was once called for Jury Duty he was dismissed for being a distraction or something.
http://www.tmz.com/2017/11/08/barack-obama-jury-duty-chicago/
heck I still remember the time I heard that Michael Jackson was called for Jury Duty, like 4 months after his acquittal.