I think if you are there first, get a drink. I think it is poor manners for an alum interviewer to not get a drink when meeting students at Starbucks. They are taking advantage of a business by using their space and not “paying” for it in any way. If they are there before you and offer to get you a drink, I would say yes (as long as they are getting one for themselves.)
My daughter had an ivy league alum interview once at a local Starbucks. The alum not only didn’t buy anything, he asked the barista to lower the music. Extremely rude in my opinion.