Well, I think your best bet would be to call or e-mail a AAA agent in your area to find out more.
I myself have never gone to Disney during a
free dining promotion, so you shouldn't take my word for it, but, for example, this is how the promotion worked for the trip we just took in January:
1. I e-mailed AAA last April through their website, got connected with an agent who worked with me throughout, and she booked a room reservation for January 2007 (the rates had not yet been announced). I made a deposit on the room.
2. In August 06, when the 2007 rates were announced, she booked a room-only reservation with a AAA discount (I hadn't decided whether I wanted a package)
3. I later converted my room reservation into a package with dining (keeping the AAA room discount because I had booked through AAA) (no charge for converting the room to a package).
4. I later changed the resort where I wanted to stay (no charge).
5. After paying the package in final, Disney announced a free hopper-pass upgrade promotion (free upgrade to hopper pass and water parks, etc.). The promotion was first offered (I believe) to Disney Visa card holders (which I am) - there was a "code" connected with the promotion (i.e. ZBWAS, or something along those lines). By the time I saw the code on DIS and had contacted my
travel agent, she had already called Disney to apply the code to my package and I was all set. My package which I had paid for was converted to the less expensive package which included the ticket upgrades.
I would imagine the Free Dining promotion works the same way. There probably is a "code". If you book through Disney, I guess you have to call and apply it yourself

If you book through a good agent, he or she should call Disney for you to apply it (although you should follow-up).
Just my thought, but are you looking for free dining for
this March? So far, they've only offered the free dining in the fall (and maybe once in January when it first came out?), but anything is possible
In any event, I would contact a AAA agent if you want to know more about it
