Only the ones that are branded Starbucks. There are a few locations that are "proudly serving starbucks) but are not Starbuck locations. Those are few and far between though. All the major coffee shops in the 4 parks are Starbucks locations and thus take the gift cards.
Bumping for a related Q - can we use Starbucks gift cards to buy non-food items at the Disney Starbucks - like the mugs in the store? Or is just on food & drink?