In extreme heat or cold the bowyer will suffer, but the wood is fine!
September is usually some pretty nice weather, so I think you are gonna be just fine. I will echo Pearlie's advice about taking it down to near-bow dimensions and having a bow ready by deer season. I suspect there are more compounds other than just good old water that need to cure out of a stave, but if you leave it unfinished during the forst deer season some of the organic conpounds will probably cure a little further still.
I had a quickie hackberry done in three weeks from cutting the tree once. I left it unfinished over winter and the next summer it just seemed to throw the arrows with a bit more oomph.