Too many references are in the show that'll be missed if you don't see the film first -- from Kira's faux Australian accent (reference to Olivia Newton-John) to (as mentioned above) the film CLASH OF THE TITANS and even how Kerry sings her songs.
As bad as the film is (I personally love it for all the obvious reasons, mostly the score), the Broadway production IS paying heavy homage to it, so it does help to know the film. Especially how the muses come to life at the show's beginning (direct homage to the film).
Of course, you don't have to see he film first, but boy... does it help you appreciate what the creators of the Broadway production were going for when they adapted the film into a musical.
One of the many Olivia Newton-John bits in the show: