I'm type I and I had a tonsillectomy at age 17. They gave me a general anaesthetic, and they kept me in the hospital for about 2 days to ensure my blood sugars were good. Once I could eat semi-normally again I was released. (Looking back, I much would have preferred a local anaesthetic as it took me nearly 2 weeks to recover from the surgery... I wasn't in pain for long, but the general took the wind out of me for a long, long time!!!)
I don't think having diabetes will make the procedure hurt any more or any less. It depends more on the complexity of the procedure and largely on your own pain tolerance. (Will they be taking both tonsils and adenoids? Do you have a chronic tonsil infection? If so, the throat may already be irritated). They prescribed tylenol 3 for me and as long as I took the meds on schedule I was in little or no pain. Your doctor will also decide which medications (OTC and prescribed) will work best for you.
Because of my diabetes, my surgery was slated to be the very first one of the day. I was told to have NO food or liquids (not even water!) after midnight the night before. (This is not diabetes-related, but surgery-related... they can't have you refluxing and choking during the surgery.) So if you happen to get low and need to eat or drink in the hours before the procedure, do let the nurses know as you might have to be rescheduled.
As it turned out, my blood sugar was high that morning (about 11 on my scale) but the nurses did not want me to have any extra insulin in case I got low during the surgery. They cut my basal insulin by about 10%, but your endocrinologist will help you decide what formula to use (if you are type I, that is).
Best of luck -- I hope your surgery goes well!

Enjoy being tonsil-free!