Yes surgeons and any other nurse or doctor can go on vacation when they get time off for vacation.
When the surgeon goes on vacation the hospital will have another surgeon available to take the other surgeons place while they are on vacation.
So the hospital is always staffed with a surgeon when they need one.
If the surgeon is needed back at the hospital for some emergency surgery for a patient then they can call that surgeon and have them fly back or come back to the hospital to do the surgery.
So the surgeon is usually always on call and can be called into the hospital at anytime when they are needed.