Some surgeons will ask for a mental exam, but many of the big name ones in the US don’t. Even Paley doesn’t do it, though he says he does a sort of spot-check during the in person consult. I know that Guichet will make you fill out forms that quite literally take a whole day to complete. They have questions about your expectations, your goals in life, your career and hobbies, how height will change your life, etc. I read that he rejected a number of patients on psychological grounds, but I don’t know if I read that on his site or if it’s hearsay. Take it with a grain of salt. That said, the whole thing about those essay forms is 100% true because I was emailed them and expected to complete them before they would schedule a consult. I admire his method but since I ended up scheduling with a more local US doctor, I never filled them out.
I know of no serious surgeons who won’t do some form of health evaluation. Things evaluated include spinal condition (I have mild scoliosis and I am still approved), blood levels for various deficiencies, medical history. Smoking history or drug use will make the doctors act very nervous very quickly.