If you do a search on "snow on Whitney in September" (no quotes) you will get lots of hits. You will read reports of people encountering snow storms from August on into the dead of winter. Obviously, anything can happen...but this is not what you are asking.
I think the probabilities are with you. I am counting on that, too, for I will be there that week also. I will check the forecast just before I go, and will have along some extra gear just in case.