They just ask to see your room key to get towels. We have taken a couple in the cooler months in the parks to wrap up with after some water rides. On the way back to our room I just put them in the dirty towel bin. We also take the towels to the room and room service will take them.
I think you should have no problem as long as you bring them back. It would be a pain to pack those just for the one day.