if you get your tonsils out, can it improve your voice?

It won't necessarily improve your voice, but it can make you less prone to sinus and respiratory infections that can make your voice worse. You would definitely want the advice of your doctor. Tonsillectomies are common, but they are still surgery, and a doctor will only perform one if it's medically necessary, not because you don't like your voice.

I got my tonsils out last year after they became absessed and I noticed no change to my voice, as did my parents and friends. I don't think they change ones voice to make a noticeable difference...