Let me take the opposing position. I supposed it's fine to leave it on when you're applying for your first or maybe even second summer job while in college because most of your life is still high school. Personally, I don't think it will carry much weight but it's not a huge issue either way.
After your sophomore year in college, I would leave it off for several reasons.
First, anyone who knows what NASS is knows that it's a recruiting tool and not necessarily competitive. Second, it may lead to questions, such as "So, why didn't you attend USNA?" [employer may think you didn't want to and then you end up saying, "I wasn't accepted." Why go there? Focus instead on all the great things you've done at your civilian college]. Third, and most importantly, once you're well ensconced in college and especially after you graduate, no one cares what you did in high school.
On a more positive note . . . you will do all sorts of great things in your civilian college -- clubs, sports, volunteerism, internships, etc. They are recent, they are more substantive than your h.s. activities, and they are done while you are an adult. That's what employers will care about. NASS was a great experience, but it's but a blip on the chain of your life.