+1 for discussing these options with the Director.
But in answer to your specific question -- yes I think it would be appropriate for the SD to
play a large
role in selecting music to accompany a
play -- consider it a type of FX. At our theater we always have some form of music to accompany the non-musicals, and in some cases, major underscoring throughout most of the
play.
Since I am not a music director or composer, when it gets to the
point where we need a piece of music created we may pull in the resident music director (who is also a composer and has a ProTools studio) to help out.
Bottom
line -- (and I'm talking non-professional theater here -- Union rules may dictate otherwise in professional theater) as SD you should be willing to get involved in anything that relates to sound reinforcement or playback for the production, including
curtain call speech recordings, pre- and post-show music,
etc ... to the extent that your skills allow.