Not going to be too much help here, but my son did both the Air Force and West Point summer sports camps back when he was 11 & 12. At that point, I think it was useful in that it fueled his motivation to attend a SA someday, and gave him a chance to talk to actual cadets, live in the barracks, eat in the mess hall and see what was there.
I don't think he actually got much out of it in terms of the sport itself (he did soccer at both academies). Certainly (at that age at least) nothing more exciting than going to any local university and doing their basic sports camp. At AF they had thunderstorms every day he was there and watched a lot of videos instead. At WP they had heat indices over 105 the first few days he was there, and being concerned about the young kids, they did limited physical stuff (kind of critical for a sports camp!).
However, if you're considering NASS, you must be a lot older than he was and if you're good (recruitable) at a sport or two, I think it would definitely catch the eye of the coaching staff or someone at the academy. You would also be able to talk to cadets (mids) and ask them a lot of questions that would never have occured to my son at 11. And of course still get a chance to be "behind the scenes" like at NASS. Different focus, but I think it would be worth it as an alternative. My biggest concern though would be with being with all the little kids - I think AF took them as young as 8 for the day camp version, but I'm sure they split up by age and ability on the field, but I don't know about in the barracks, etc. I know my son wouldn't want to go back and do it again now (he is doing NASS) - he'd consider it more for younger kids, but that may be just because he went so young.
Good luck on getting into NASS in the meantime!