I was 19 when I had the operation on my lower jaw. So that was nearly 40 years ago. I can't believe it was that long ago!
I had quite an open bite and my top and bottom teeth only met at the back teeth. Although the dentists never said this, I often think that a certain bad habit that I couldn't totally give up until I was 17 didn't help! I think my namechange gives a clue to what it was, ha ha.
But seriously I think both you and your son should think some more about it.
Back then I wasn't asked to wear a brace for months beforehand. A while before the main operation I just had some teeth taken out. Then a day before, had metalwork glued on top and bottom teeth.
During the operation I had bone removed at four places in bottom jaw. Was meant to stay in intensive care for one night but spent a few more days as after the operation, splinting fell apart as braces wasn't glued on properly. Also imagine throwing up whilst wired up. Bit scary at the time.
You will have numbness to your lips as they cut through a facial nerve. This means a bit of drooling at first but it got better over time. I remember going back to college wired up and having to be careful not to embarrass myself!
A year or so later had to go back under the knife to reshape my chin as I had uneven edge due to previous operation. So the numbness lasted for a few years but it did improve as the nerves knitted back together.
The main issue is that your face changes. I was warned about it. In fact the surgeon said it would take me about another 19 years to get used to it. My face used to be long but is now shorter and I have a squarer chin, but I put that down to the issues with the operation and the second one.
After all this time, I don't regret having it done. It saved me from not being able to chew properly later on In life.
You and your son should think carefully about having the operation. Is your son's overbite that bad. He should only do it if he really needs it rather than it would be nice to have it to improve the look of his teeth.