There’s two general opinions floating around. One is that you need to take time off. It allows the body to get back to neutral, recover, and heal. You gain external rotation and lose internal rotation (this does create velocity and it’s one of the reasons why you see guys throwing harder mid-season then preseason, because of the gain in ER). However, losing internal rotation also creates its own problems. Along with that its very difficult to strengthen and correct bad movement patterns when you’re always throwing and putting yourself in them. For example if you have a lot of lower back arch, or poor scapular control when you throw and you’re trying to correct these bad patterns and develop strength in the weight room to have more stability you’re inhibiting that effect by continuing to throw and move in ways that are counter to what you’re trying to change. Being a college pitching coach and strength coach I’m a big advocate of this approach as I feel a month or two off is necessary to develop strength and allow the body to heal. Here’s two articles (really one broken up) by Eric Cressey, one of the top performance coaches there is.
On the flip side of that you have the school of thought that it’s under training that is killing pitchers and I do believe this is why there are a spike in injuries come spring training, or the beginning of a high school season. Pitchers just don’t prepare properly for the demands that are placed on them. By training year round you keep your body prepped and ready for those demands and reduce the risk of injury. Here’s a great article by Driveline on why to train year round.
Really you need to make the decision on your own based off your sons needs. But just to throw my two cents in there , my opinion would be to plan your training appropriately. Take two months off but make sure that time off doesn’t leave you with only a month to prepare for the next competition season. But make sure to stay training in the weight room during the off season. Playing different sports is also important. Multi-sport athletes are sometimes more desirable and tend to be more athletic since different sports train different movement patterns. A lot of this also depends on how old your son is.