You can use the app to pay for drinks, but can't redeem rewards or coupons (as figment mentioned above.)
I always redeem my award (should I have any) at the Starbucks in Orlando International. It started as a tradition - I'd always stop there as my "last good coffee" before choking down the Nescafe. Now they have Starbucks and Joffrey's, but I still stick with the tradition.