Unless you use a Disney Vacation Account. For those you need to call DCL yourself and make payments. You can add the Disney gift cards to the vacation account and use that to pay Disney. If the account is open 120 days or more, you ill get a $20 Disney gift card as a bonus for every $1000 you spend on your Disney vacation.
If you just have a few gift cards to apply (and not a DVA - although I highly recommend the DVA), just call Costco and they in turn call DCL with your gift card numbers. Easy!
GET UP TO A $1000 SHIPBOARD CREDIT AND AN EXCLUSIVE GIFT!
If you make your Disney Cruise Line reservation with Dreams Unlimited Travel you’ll receive these incredible shipboard credits to spend on your cruise!