Another AirTran customer who had no problem with getting the DME bags brought right to my room. (Although, my understanding is that no airline has problems with this process since it's actually the airport baggage handlers who pull out the yellow tagged bags and put them on the Disney transport trucks.)
You should know, however, that AirTran isn't a participating partner for the "return" trip to the airport after your vacation. You'll have to bring your bags to the DME bus and have the driver load them underneath. Then you'll need to check them in at the airport with AirTran.
That said, you can have the CMs at Guest Services/Lobby Concierge at your resort do on-line check-in for you 24 hours before your flight. I've heard they'll even print your boarding passes for you.
Good luck!
Eileen