I don't know for sure, but I don't think it would work. Probably like the AP rules, the person who's name is on the card, whether it be the AP card or the AAA card, must be included on the ressie. So if mom's not going with you, I don't think it would work.
A AAA membership is relatively inexpensive - I believe no more than 80.00. If you add up savings you'll get if you have one, I bet you'll more than make up for the cost of joining. You can get great rates on car rentals as well if your planning on renting a car.
To follow up what travellady said...my AAA fees are $54.95 for me and $30.00 for each additional driver. I don't know if they vary from state to state...but IMO, it's a good investment all around (not just for Disney discounts!)
Edited to add - We just reserved our room at Pop Century, and the AAA discount saved us a little over $200.
Thanks everyone. I just saw on our AAA website for Washington that they have a special to add a member for half the price so I am going to see about doing that.