I catch and pitch and only started catching regularly in the Spring/Summer of 2015. If he's committed to getting better and actually wants to play the position I'd say it's worth it to give him a shot. I saw some of the above comments regarding how catching skills take years and years behind the dish to develop, but if your son has a high baseball IQ and a natural feel for the game he'll catch on quickly. I've found that it is very much a reactionary position as much as it is an anticipatory position. Just my $.02
edit: worth noting that I've only pitched one inning this year and if I don't catch I play corner outfield or middle infield. Full time pitcher as well as being "a whenever I'm not pitching catcher" is a pretty ludicrous idea.