They sure do. Typical discount is about 10% off of rack rate sometimes more. I always search AAA, AARP and anyother rate I can find, do a spread sheet and compare weekly.
Worth the effort.
I already reserved the GCH for 3/17-3/19. The best rate I could find for the days we needed was directly on the Disney website. I clicked on a link that said "up to 35% off", but then when I booked it said "we're sorry the rate you selected isn't available on the dates you selected" -- but then at the top of the reservation it said "Winter Hotel Special" or something like that. I have no idea what kind of rate I got. We've stayed at the DLH many times, and the PP once, but always with a package so it's hard to compare prices. This time we bought the 3 day hopper online special for $149 each, so it was better than the package. Maybe I'll call Disney Travel to find out what the rack rate was, if we got any price break, and if they offer a AAA rate and if it would be better...