When I booked my husband, son, and another couple under the AAA rate, I had to book hubby in one room, my son in the other room, and split the couple up and had to give my hubby's AAA # for one room, and my son's AAA # for the other room.
Once they arrive, they will sort out the rooms at that time.
So, in answer to your question, this particular CRO agent I spoke with required a AAA # for each room booked. However, as is often the case your experience may differ with a different CRO agent, or if you book directly with AAA
Carol