There is some risk for any procedure. For tonsillectomy and for many surgical procedures the main risk is a bad reaction to general anesthetic. Different people respond differently to medications so an anesthesiologist will closely monitor patients during surgery but even with the best care there is some risk. For young healthy patients with a good standard of care the risk of death from general anesthesia is about 1:250,000. You are probably in more danger of dying from a car accident on the way to surgery than from the surgery itself. There are also risks from bleeding, blood clots, and infections. You and your doctor should carefully consider the risk:reward ratio of any procedure. If there is little risk and a significant benefit than it is a good choice; if there is high risk and/or little benefit than you should avoid it; if it is in the gray area than think long and hard and seek a 2nd opinion before going through with it. I had surgery last year (anterior cervical discectomy and fusion). My surgery had a success rate of 94% so it was a pretty easy decision for me.
What filletofspam said is all correct.
I might add that your age being 41, it's going to be tough on you. (just as they say, it's hard on adults) I had mine out at age 27 and it was rough, but well worth it.
I assume yours are giving you trouble as mine were....infected, blah blah chronic tonsillitis. I had felt like crap for a few years because of it, but once I got em out and healed up, I felt so much better.
I'd say if they need to come out, then go for it. Nothing wrong with getting rid of a problem. Just remember that you will most likely need more time to heal because of your age. I'd square everything away with work before hand too......make sure they will give you the time off.