Short answer:
No, it won't.

Long answer:
This mod can't make multiplayer server crash for the simple reason that this mod only contains songs. The songs (unless they're very badly done and untested) cannot make crash starbound at all. The song mods aren't even required to be in the server's mod folder to work because songs works client-side and are streamed. So, not only people can play these songs on any server, but they will be heard by anybody, regardless they have the mod or not. Though, if they want to play the song with you as a band, they will need the mod so they can select the song used. No matter what, a song, or a mod containing only songs cannot crash a multiplayer server.