I'm not sure, but if it's a standard Disney Gift card, such as the ones that you can buy anytime, it should not have an expiration date at all. And yes, you should be able to use it to renew your AP.
You can go to www.disneygiftcard.com for more info, and a FAQ section. Maybe that will answer your question.
I know for a fact that there is a law in California that GiftCARDS are not ALLOWED to have an expiration date on them (Gift CERTIFICATES, yes, but not cards). They sell the Disney Gift Card at Disneyland, and it's a generic "Disney Gift Card", so I assume that is the same one they sell at WDW too. If so, it has NO expiration date on it.
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