Yes. But...
Make sure the gift cards are fairly high value. The upgrade will be about $208, including tax. The ticketing system allows only three methods of payment for each transaction. Each separate credit, debit, or Gift card is considered a separate method of payment. So, for example, two $100 gift cards plus the remainder by cash or other method would work, as it is only three payment methods. But using four $50 Gift cards plus something for the remaining $8 would not work as you are now using five payment methods and the system cannot handle this.
A way to get around this will work only if you are staying at a Disney owned and operated Resort. You can put the upgrades on your room key as the Resorts appy each separate Gift CArd to your account as a separate transaction, and there is no limit on the number of transactions.