You are a bit unclear what you are doing because of some of your terminology- songs, styles, registrations, variations are all terms that seem randomly used.
Styles are built, edited and saved in the style creator and this does not use registrations. If you are working in style creator it is up to you to balance volume between instruments and variations an$save it this way.
Song set ups (not songs) are saved in in registrations, where you can save different styles, style variations voices, effects etc to match your arrangement of a song. I think this might be what you really mean.
The term ‘song’ is usually referred to mean a recording.
Maybe you can try to restate your question more clearly.
Mike