How often do GA pilots use the Autopilot approach feature while landing?
It's a perfectly acceptable practice, provided you disengage the autopilot upon reaching minimums and hand fly it the rest of the way.  Some manufacturers, like Cirrus, recommend flying a coupled autopilot approach.

I won't sit on the fence about this.  Learning how to fly coupled autopilot approaches are fine, but I insist all my students learn how to hand fly approaches, both as part of their initial instrument training and for all instrument proficiency checks I administer.  If I were an examiner I would insist on seeing instrument applicants demonstrate hand flown approaches on their checkrides as well.  

Autopilots are great but their use can begin to atrophy their flying skills and it can come back to bite them, particularly in an emergency.

As to the exact numbers of GA pilots who fly coupled autopilot approaches, that's probably going to depend on the pilot and the equipment in his/her aircraft.  Pilots with autopilots installed are probably going to be much more likely to use them and be more comfortable flying approaches this way.