If you're staying more than one night, don't wait until the last night to apply the gift cards.
Also note that they will run the card once the charges meet a certain threshold, so you might want to go pay every few days with your gift cards if it's a long trip and/or you're spending a lot.
Worse case scenario, if they have ran the charges, they can reverse the charges and use your gift cards instead.
But odds are if you go following the Christmas party you'll be fine.
As PP mentioned, they do run the cards if charges hit the predetermined limits so depends on how long your trip is too. We've only hit our limit earlier than check out on long trips, those longer than 10 days. Usually it's just at check out
Go straight to the front desk when you get back to the resort to settle it. We were at Epcot late because of the Wine & Dine Half Marathon After-Party, and I know my friends charged stuff to the room at the party and were able to have it covered by gift cards on their way back to the room immediately after the party.