Once again. The confirmation code you get from AA Hotels is only useful to AA Hotels. It has nothing to do with these hotels' own IT systems. Giving the hotel the AA Hotel's confirmation code will only lead to confusion on their end. It is meaningless to them. When AA Hotels confirms the booking through the GDS system, these hotels will then generate their own confirmation number associated with the reservation. Which is not the one AA Hotels gives to you at the time of booking.
With some hotel chains, on the day of the actual check-in, AA Hotels will give you that hotel's confirmation number (the one the hotel generates) in the "what to do today for check-in" email.