We've been saving our Disney Reward Dollars just so we can stay at Aulani. Help to offset the huge cost of a few nights at the hotel. We don't own there.
I'm gonna go out on a limb & say it probably would work just like on the DCL's or any other charges like you would make at the parks. You can charge an excursion to your room and then just apply the gift cards to your room charge. I'm not planning to pay Disney for any excursions but will likely have any meals on site or spa treatments or cabana rentals put on our room charge - then I will take our gift cards down & have them applied to the balance.