They will pick a QB, especially after their GM and Head coach gets canned
Neither of them will get canned. They never, ever, fire GMs and they invested too much in McAdoo to fire him after one year when he made the playoffs his first.
Despite how little of it is really on him, Eli is the only big piece that will be gone (he has a roster option that makes it possible, even if it has a cap hit to it) and honestly he'll probably be better off for it anyway, assuming Denver or Jacksonville pick him up.