Yes, you can, but you must call AAA directly and book a package which includes park tickets. You cannot add the DDP to an AAA rate room booked directly with Disney or with any other
travel agent. Only an AAA agent can get you the DDP (which you'll pay for) plus the AAA discount.
I've done it before and we're doing it again this July.
We're saving close to $400 off 8 nights at the Polynesian, and we're getting hoppers and DDP for 5 of us. The AAA discount is a percentage off the room portion of the package. But again, you must contact an AAA travel agent directly.