YES!!! My daughter was 2 1/2 and the exact same scenario. My mom waited until I was 18 and I agree, it was awful!!!
She did 100% turn around, she recooped in a few days, it was a hard few days of some pain but they managed it well and they kept her over night (I strongly recommend this as the nurses can really keep close tabs on her those first 24 hours and you can bunk in the room with her!!). But she slept like a DREAM afterwards! She went from sleeping horribly, to getting sick all the time to rarely ever getting sick and hasn't even missed a day of school this year. The sleep thing was the biggest issue for us as she had sleep apnea too. The biggest thing they will say is to keep her hydrated after, even if it hurts to swallow.
I strongly recommend if they have said twice and her tonsils are enormous do this for her relief. The sleep issue alone can cause so many problems for little ones.
They bounce back a lot faster then we did at 18 I promise!! My daugher was up and about like normal by the sixth day 100% herself. The first few days are the hardest but if you stay overnight at the hospital they will get you through the worst part of it. I had my daughter sleep with me and I kept the pain meds going so she never got to the point of bad pain and kept her hydrated.
If you have no history in your family of issues with anesthesia then more then likely it will be fine. Have her take her favorite toy and they will let it go in with her. My daugher took a doll and they put a hair net on the doll and a wrist hospital band too!
They will allow you to remain with her until she is asleep and be there when she is waking up. It is hard when they first wake up, she will be disoriented, scared, in pain and out of it, but you being there will be priceless for her.
Hugs, it is hard to think of surgery but this literally was a positive choice I made for my daughter that young, she was even younger then yours! :)