Technically, no, but I don't know how the Federal "Gun Free school zone" law would effect you in New Hampshire with not having a New Hampshire permit. I may seem too careful here, but there appears to be an implication that having the permit from your home state exempts you from that law in that state, whereas a non-resident permit would not. There a few current, if not recent, threads worth looking into here in the subject.
If you have the $100, it might be worth it to get it.