MEM,
I first checked availability on the dates I wanted, and once he told me rooms were available, I asked if there were AAA discounts available. I know they block off a certain amount for these discounts, so it is possible that not all would be available at the discount. They don't ask for a AAA member number, but you should have it available when you check in.
Something else I learned last year was that because we didn't decide on a date until much closer to the time we wanted to go, there were no AAA rates available - or so I thought. It turns out there were no discounts available for the entire stay of our trip. We checked in on a Saturday, and it turns out only Saturday wasn't available. When I checked for just Sun - Friday, there were discounts. I ended up having to make 2 separate reservations - one for Sat. at normal rates, and one for the rest of our trip at the AAA rate.