When I brought my DIsney Rewards Card (which works like a gift card) to Guest Services on the Magic last week, I was asked explicitly how many of its value I wanted to use, and was able to apply the exact amount I had outstanding on my onboard account. After making more purchases, I went to Guest Services and applied the remaining amount on the card.
If you are making an onboard booking with the agent (rather than just filling out a request form and placing it in the box), you can certainly ask about using a gift card for the deposit. The request form asks whether you want to use the same credit card as you have on file, but the deposit is not actually charged to your onboard account -- it's a separate transaction. If the reservations agent puts the charge through immediately, then it should be possible to use a gift card, and it shouldn't matter if its the same card you're using for your onboard account as long as it contains enough money. I have always used a credit card, though, so I don't know whether the charge is processed immediately.