I believe it wouldn't even be legal for an unpaid intern to be used for "actual work", as they're supposed to strictly be involved in mentoring/training activities. Hopefully Square knows that, and wouldn't try to treat its employees unfairly in the first place. They seem like a great company.
Programming internships are typically paid positions. I can't speak for Square, but every other programming internship I'm aware of (even at other startups like Path) were paid.