2 answers
I personally don't think it will. Every competitive college is going to have the typical applicants with NHS on their activities list. Every kid is going to have something to say on how they spent X amount of hours on NHS. If you think about it, if you're the one kid that doesn't, it makes you stand out. That can be a good thing too if you're strong in something else, let's say Academic Decathlon Team. If you don't have NHS on your application, it's not like colleges are going to notice that and say "Oh, this child can't be a part of our school because they didn't participate in NHS".
So depending on dream school if it is an Ivy it might bump you down a little but any non other ivy caliber schools such as Oregon Oklahoma SUNY Binghamton it will not matter NHS will only boost you there a lack will not hurt you.
It’s like going on vactation with an additional $100 dollars good to have but not necessarily needed.