Sound energy is broken up into two over lapping energies;
Percussive energy, which is the bass energy that is felt in your body. Deaf people experiences this just like everybody else, so for example, there's nothing stopping a deaf person going to a night club or a very loud techno gig and dancing. Also in that respect bass heavy music (dubstep, techno, dub and hip hop etc) would be the most interesting to "listen" to as a deaf person.
And Acoustic energy: the stuff that you hear.
So Eamonn while you have the right idea about deafness and Percussive energy, Percussive enegry is considered part of the sound energy (and music), so it is more correct to say a deaf person is not listening to the music, (one doesn't listen to percussive energy, one feels it) but that they are still dancing to the music , not as you say, to a by product of the music.
It's just their dancing to the part of the music you don't listen to, but feel.