An unaccompanied song is just that - unaccompanied. There are people who sing unaccompanied simply because they can't play anything but a genuine unaccompanied singer puts over the rhythm and the melody of the song in their own special way and no accompaniment is needed. I don't sing unaccompanied very often, but if I was and someone started to play I would stop singing. (Thinks - perhaps this is why I tend not to go to sessions!)