I have heard that Disney is starting to crack down on unauthorized use of discount codes, though I have had no personal experience with this.
This may differ if you book through AAA. I would not take the chance of having my room changed to rack rate. Bring the card. I've booked AAA rates in the past but don't remember if I was asked or not.
If there is a problem with your reservation when you get there, you will really want your card.
Better safe than sorry.