Hi rondohandles. I've been a neurosurgeon for the past 2 years now and I get this question asked a lot. As a general rule, yes, they will shave either a spot or all of your hair. I know that most people tend to shave the whole thing just because a bald spot at a strange spot on the head will look strange. So I hope that answers your question. Best of luck with the surgery.
May I ask what kind of surgery you are getting?
EDIT: Woah what just happened!? I just got 13 TPs in 5 minutes!