I tried this last Saturday. There's a Starbucks inside a DoubleTree so I figured it would work. However, it wouldn't work for gift cards because they didn't have any--as the person working there explained, they're not an actual Starbucks franchise, they are operated by the hotel, and they don't sell gift cards. It's possible YMMV but I suspect that any Starbucks that would work for the Hilton credit is not going to have gift cards--if anyone has contrary data, I would be happy to be wrong.
I thought about getting a Starbucks drink but decided to test what
@afan mentioned and get a soda at the gift shop. I was pretty certain it would work since I had to pay for it at the check-in desk. And the charge shows up as "Hilton" something or other. But so far no credit (the charge posted Monday).