If you can synchronize the C:\Users\<your username>\AppData\Local\Packages\41730Zubersoft.MobileSheets_ys1c8ct2g6ypr\LocalState folder between devices (and that's the storage location you have listed under Settings->Storage->Set MobileSheets Storage Location), then yes, you could accomplish what you are describing. You would just need to perform a file sync on each device to get the latest database file and any new or modified song files. The database file must be loaded in that directory (it's a limitation of the SQLite library for UWP applications), so at the very least you have to sync that file. If you want to sync multiple folders, then you can use whatever folder you want as the storage location.
Mike
Mike