Good question. Here at 6000 ft elevation, they will continue to send out side shoots even after the first frost. I usually get sick of broccoli and let them flower for the bees. The broccoli is one of the last things blooming in the fall.
I think it will depend on the variety and the climate.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-