Bitcho,
No, very few courses close down in September. In fact, they all do on Mondays for obvious reasons so I'm sure a few are going under the knife today, but I can recall playing courses deep into October that haven't shut down yet. And that's the best time to play them - still fairly cheap and the greens roll about as nice as they will all year as they are pared down and fast.
I am familiar with Bear Creek, never played it. I am lucky to have multiple friends with Troon Foursome passes and "ins" to some pretty sweet courses around town, so I generally stick to those tracks.
EDIT:
link. I am a little bit wrong about the courses, way more are shutting down this week than I thought, but the one I live on (AZ Biltmore) and a muni I play at (Papago) tend to shut down pretty late relative to the others, and this year is no exception.