I have never heard of this! There must be a reason they put pups under anesthesia to pull teeth. All I can say if you let him do it, pooor Bailey! I know that when Tinkerbell's teeth were falling out in the back, they were very sensitive and she would cry a little if I messed with them. The caps were hanging on causing a terrible smell because of food stuck in them. They really seemed to hurt her when I would try to mess with them. Please try to play games and such that will allow them to loosen on their own. I can only imagine how much Bailey will like your fiance if he pulls his teeth out! I have a feeling yorkies don't easily forget.
My last dog had a couple of teeth removed when she got older and it was only $150.