I've never used a gift card for the lockers, but they do have a place to swipe a credit card, so I would guess that would be the same place that they'll read the gift card.
Yay! thank you, after I asked I finally found an official page that says you can't, but it also says that vending carts don't take cards, and I know that's not true.
I saw that in the terms and conditions as well and was a bit puzzled by it. I knew the lockers had credit card readers and all of the Disney-owned places that I could think of that take credit cards also take Gift Cards (notwithstanding the times when the system is down - but that's a different issue). So I figured it would be worth asking Guest Services and see what they say.