At this point, I'd be shocked if management kept Peterman on the roster past Sunday. They have to let this guy go. He's become toxic, and a national punchline, for his insane 13.3 INTs to passes. He throws interceptions in his sleep.
Hate to see anyone's career disappear in flames, but there's no way this team can ever trot Peterman on the field again from a PR perspective. If Allen isn't ready to go, could you imagine the collective WTF we'd all give if Peterman lines up behind center against Indi?
It also makes no sense to keep him, strategically. You keep three types of quarterbacks on your roster IMO:
Future/current franchise players, like Kelly and Allen.
Stopgaps, like Bledsoe, Flutie, Taylor and Fitzpatrick--guys good enough to win more games than lose, with the right offense, but who will never bring you far into the playoffs.
Oldish veterans like Derek Anderson and Kyle Orton who lack franchise talent but truly know the game.
Peterman fits nowhere in this model. He's not the future, he can't win games now, and he actually loses games that were his to win.