No, your secrets are safe from the dentist. It'll be just like normal sleep, not like hypnosis when you would certainly talk.
But I wouldn't worry about it. The CIA and DHS are already scanning your brainwaves so they can read your deepest thoughts. The only defence against that is to wear a foil cap. (The lady in the picture has a rather stylish one but you can see by the fear in her eyes that she's not sure if it'll work.)