Is there anything else he wants to try? I would hesitate about putting an 11 year old into an offseason program specifically for pitching. It's good to get a mental and physical break. As far as what you should have your son do, I think that it would be better (and easier for you) to find another semi-structured sport to have your son participate in for the off-season.
Judo or wrestling
Track and field (some areas have winter indoor seasons)
Speed and agility training (some places have bi-weekly group classes for kids)
I am a pretty big proponent of the boxing, kickboxing, Judo or wrestling options. Apart from the obvious physical benefits of increased strength and explosiveness, these activities teach skills that are always going to be useful. Fights happen, and it pays to be able to take care of yourself.
If you have any questions, let me know.