For many, many trips I checked in online and the balance posted to my credit card. Then at some point, at my leisure, when I walked by & saw the line was short, I would go to the front desk. They would reverse the charges off my CC & apply gift cards to that balance. I did this many, many times. Then someone on the DIS suggested I call in & apply gift cards before my arrival. Done!
I did it about 2 days before arrival & it worked like a charm.
One word of caution though, when you pay for anything at Disney & there is a refund for any reason, the refund goes back to the original form of payment, including GC. It goes back to the exact same GC # it was paid from. So, hang on to those empty cards for a bit after the trip before disposal.
You always think there's no reason you'll need a refund & then you do. Its happened to me & its a hassle if you don't have GC any more.
If you're like me, you collect small amount gift cards over time (so its not as painful financially). You can register the card #'s at disneygiftcard.com (on back of card) and can combine down to one # used to pay room balance. This will help the call go faster & you only have to keep one for refunds.
Many like to register the cards so they can move balances to another card quickly if lost or stolen.