I certainly wouldn't feel the need to mention it to the dentist, nor to the doctor unless i was consulting him on something scalp-related. There is no reason why a doctor would be any the wiser unless he had some reason to poke around on your scalp. The dentist is somewhat different, because your face is under very close scrutiny in very bright light. On the other hand very bright lighting can make a lace system more invisible, rather than the other way around (that is not true of skin systems, which is another reason why I prefer lace). I have been to the dentist several times during the time I've been wearing, and if the dentist or his nurse spotted that I'm wearing they didn't give any indication. But honestly I don't really care - they are medical professionals, used to seeing private sensitive stuff and bound to discretion. I don't know them socially. If they spot something, I can live with that.
If you have to go to hospital for something head- or scalp- related then you have to tell the medics, and maybe in some cases take the unit off. I have never had to do that, but the issue has arisen before on this and other hairloss forums. The general view from posters who have done this and from medical professionals is that doctors get this situation not infrequently, and are sensitive to the issues. The advice is to tell the doctor confidentially about the system, and if you have to take the system off, arrange to have a surgical cap available to cover up.
Of course, there is always the remote possibility that you will have an accident involving a head injury, and you will be taken to hospital, possibly unconscious, and you won't have control over what happens to your hair system. I hope that never happens, but if it does I will have bigger things to worry about than hairloss or the confidentiality of my hair system. I take that risk willingly. In the final analysis you have to have balls to wear a system - it's probably not for someone who would die a thousand deaths if anyone ever discovered.