Is a shotgun shell too large to fit through the mag well? (I don't have an AR to test.) I've seen a belt fed one on YouTube but as far as I know it isn't available for sale and was still a little buggy.
I don't see much purpose in a shotgun ar upper myself. There are plenty of semi auto shotguns, most can have a pistol grip stock added if desired. Just my personal opinion of course, I would like one of the nice semi auto's one of these days.