Rats can do NCAA sports. There is, or at least used to be, a bit of friction between NCAA athletes (dubbed "permits") and the rest of the Corps. Usually, it stems from the perception that the permits do not have as difficult of a Ratline as their non-NCAA counterparts. Note that I said "perception." The reality is that NCAA athletes get dogged at practice while the other Rats are doing Rat Challenge or other physical activities. Unfortunately, the rest of the Corps doesn't see that, so there tends to be an attitude that the permits are getting out of stuff (or, in VMI vernacular, are "worming" out of stuff). There are other things as well, like NCAA Rats eat dinner with their team as opposed to with Cadre, and in-season athletes often are excused from things like parades. The perception is that the NCAA Rats have an easier time in the Mess Hall (which tends to be pretty stressful), and again, there is perhaps a general attitude that the permits have an overall less difficult time with the BS that is daily life as a Rat.
I'd venture to say that the reality is quite different than the perception, but that maybe there is, as with many stereotypes, at least some modicum of truth to bolster the negative image. Football Rats have intense practices, no doubt. So do Basketball and Track Rats. Golf and Rifle Rats....well, maybe not so much. I'm sure rifle shooting is difficult, mind you, it's just not necessarily the most physically demanding sport. As long as your son is prepared to catch a little sh!t from his Cadre (or perhaps more than a little), he can participate on the Rifle Team and will do fine. The upperclassmen on the Rifle Team will be good mentors for him (and maybe his Dyke will be on the Rifle Team).
Interestingly, and this is purely anecdotal, I often noticed that there were a ton of Rats on the Rifle Team, and not so many upperclassmen (there were a few, of course). Granted, the natural course of attrition takes its toll; however, one couldn't help but notice several former Rifle Rats who, upon getting the freedom to be less active as an upperclassman, all of the sudden decide to drop the sport (non-NCAA/non-club upperclassmen, in my day, only had to do a mandatory "personal workout" twice a week). It doesn't hold true in all cases by any stretch, and I don't mean to point out anything except from where the negative perception can originate. I think it's just something to keep in mind.
If your son wants to shoot on the Rifle Team, he most definitely should.