Think about this logically. Broadcom has to do some analysis on who to let go, who to keep and who to transition well before any actual closing. They can't simple wave a magic wand and get this info instantly at closing date.
They have to prepare for the potential severance packages, prepare payroll transitions, prepare offer letters etc. etc. It is a huge task to do this for thousands of people which is why they obtained the compensation and address details a few weeks ago. This analysis is probably ongoing or done at this time and your name is probably already on some list that isn't public.
My take is this info is going to be made public even to upper management only very near the closing date.
The closing absolutely can happen anytime between Sep 15 - Oct 31. I would say anytime in this date range is fair game.