Yes it's entirely sung-through like the stage version, although there are a few occasional spoken lines which I don't remember from the stage or concert versions. I think these are there to clarify the storyline and/or are ad libs from the cast, especially Sacha Baron Cohen who adds in a couple of one line jokes.
I was looking forward to seeing a film with no spoken words to be honest. Still good film though. I thought SBC wouldn't be suitable for the film but he was, a bit like Jimmy Nail in Evita.