When you check in, you will need to give them a credit card for your room charges, but you can go to the front desk at any time during your stay and pay off the accumulated charges with the Disney Honeymoon Registry gift card.
If you wait til the end of your stay, they will charge your credit card sometime during your last night and put your bill under your door, but you can go down to the front desk on your way out and have them back the charges off your credit card and apply the gift card to them.