Yes. If you book directly with disney and request a AAA room rate, you will have to show your membership card at check-in. If you can't produce a membership card, you lose the discount and must pay the full rack rate. So in short, don't forget your card!
I saw you said "rooms" plural. Check with the hotel if each person needs a card, or just one if you are going in a group. I know with Disney not everyone in each room needs a card -one member is allowed to get the discount on up to 3 rooms at once.