Yes, she to he can, and no; I don't think you need a primary phsician's note. New regulations regarding health privacy dictate that your employer can't ask. its best to get a few days off for personal reasons, then get a plastic surgeon to say: you had surgery and can not go to work until the day your surgeon deems you can sit. See a board certified plastic surgeon who does a ton of BBLs and you will be in good hands, good luck.
Your surgeon should be able to provide a note, but keep in mind that your surgeon cannot lie. This means that he/she can be vague, but cannot say that you had a procedure that you did not have.
Best to ask your surgeon for a doctor's note after surgery. He will be the best to assess your progress. Good luck.