I don't think it's that hard. I mean not reading music doesn't mean that an actor can't see the basic structure of the song.
When I was a musical director for a show in college the actors were able to tell when the notes went up or down for example. They recorded me playing during music rehearsals and learned by listening to that.
Plus, if it's not a new show there are always recordings to listen to. My show was Godspell, so the cast came in pretty much already knowing the vocal parts.
....but the world goes 'round