I have no idea, but I guess he won't play. Mike McCarthy says Rodgers hasn't even thrown a football this week:

(Was Rodgers able to throw more than a tennis ball today?)
We didn't even go that route. The plan was to rehab him as hard as they possibly can with yesterday, and he was a little sore from yesterday's work today, and that was the same plan today. They're working as hard as they can to get as much strength back in the shoulder. That's the focus.

Will Carroll is the guru of sports injuries, at least in the media, and he says Rodgers should be a game time decision:

Let's get past the semantics on Rodgers. He said that he'd separated or dislocated his shoulder just after the game, while coach Mike McCarthy denied it. On Monday, the official word was that Rodgers had suffered a sprained shoulder. Anyone want to guess how? In a separation or dislocation (it's the same injury, just a matter of degree), the AC joint is stressed and if the ligaments are sprained ... well, there you have it. The result is the same. Rodgers will be sore, but his response to treatment and any loss of mobility or strength will work against getting back out there on Sunday. We won't know how that works until he gets back out on the field and throws, which likely won't come until later in the week. He was very limited at practice on Wednesday, a bad sign. My early read on this is that Rodgers will be a gametime decision on Sunday, so the Packers and fantasy teams should have backups ready