Do holistic doctors work?

Yes, certainly. I and many other holistic doctors work very hard for the benefit of our patients. In most cases, we take more time with each patient than our colleagues in more conventional practices. This does not mean others cannot practice with a holistic (whole person) intent, but i'm speaking here of physicians who have identified themselves as "holistic doctors.".
Proven vs unproven. By definition, "alternative" is different than modern western medicine. Generally any drug, herb, treatment, or procedure that stands up to rigorous scientific scrutiny is included in modern medicine. The problem is that many alternative practices, herbs etc do not stand up to scientific scrutiny and cannot be shown to work. They therefore remain "alternative". Be careful and watch your wallet.
Yes. Many doctors are md's and holistic or dentists and holistic.