Water sources would be your first problem...monsoons end sometime in September usually so that by November, many water sources could be dry.
There are many high elevation sections before you hit the Superstitions (talking 8-10,000 feet), so if winter comes early, there could be some good snow storms. If no snow, expect freezing temps at the higher elevations.
Finally, the AZT still does not get tons of hikers in many parts, and those that do hike generally go in the spring. Expect a solo experience in November.
In 2009, a thru hiker named buck30 did the AZT after he finished the PCT. He hiked southbound, but you may find his experiences helpful in planning a fall trip. The link to his journal on postholer is below:
http://postholer.com/journal/viewJourna ... ent_id=534