Yes! I had received some as gifts, put them into the app and they sat there for months and months (I don't drink coffee and don't go to Starbucks). We went into the Trolley Cafe in Hollywood Studios and found the most adorable cupcakes. They, of course, were a bit pricey but my children loved them. As it turns out, they accepted my gift cards through the Starbucks app so we all got a cupcake and a drink for 'free'!!!
I don't have experience first hand with this aspect but I have read that they may not honor special promotions like your free birthday drink or something like that but definitely gift cards are aok!