I am a dentist working in dental sleep medicine. This is a very interesting question. In fact, I have never seen it posed before. I can give you a general answer that may also be applicable in this case. The general principle is that you never aim pressurized air at a fresh(unclosed) surgical site inside the mouth. In addition to pain, you run the risk of introducing an air embolism into the body. This goes for an extraction site, a surgical site, or a newly placed dental implant. Some sources would be a dental air syringe and a high-speed dental drill. Since CPAP air is, indeed, pressurized air, I would think that the same would hold true for that, speaking logically. Arthur B. Luisi, Jr., D.M.D.
It started three days after tooth extraction. Woke up in the middle of the night throbbing pain. I took the cpap off pain went away after about twenty minutes. Went in day after to get packed for dry socket. That eventually went away. But pain from the cpap still is hanging around. My apnea is pretty mild, so I'm not really worried about not using my machine for a few nights. I'm pretty good with pain. I only took two of the pills out of the bottle they gave me. But that dry socket is pretty intense. I'm sure it will all settle out in a few days. I got my wisdome teeth removed little later than most do. My guess is most have that done long before developing apnea.
I'm so sorry you experienced a dry socket. Those are really painful!
I'm 66 and had one of my 4 wisdom teeth removed last year about this time. It had broken in half, down to the root. Once removed, my nighttime TMJ dental device shielded the area from CPAP pressures and air and I didn't get a dry socket, so I went through it all very well. Only trouble was, the wisdom tooth that was removed was an anchor tooth for my bite. When it went missing, this threw my jaw out of alignment once again because of bite changes in the daytime. So, I got a lot of pain from that. My TMJ dentist fixed the problem for me and I was pain free and only a few hundred dollars lighter for the adventure. I hope I get to keep the other 3 wisdom teeth!