Anything's possible
but it wouldn't be easy.
It could work as a Moulin Rouge style piece. Movies do not HAVE to be realism, despite the fact that that's the way the genre is moving. Chuck realism out the window, let go of the staging (As anything written for one medium will never perfectly translate to another) but keep the intentions behind it. If the musical uses lightbulbs descending from the ceiling to be stars, that's fantastic, but don't replicate it because it'll look frickin weird on screen. How would a movie replicate the feeling and the significance of that moment, in movie language?