It sounds like you're talking about a 2-nite backpack, and if thats the case then you'll be fine. The trails aren't any more crowded that week than they usually are, but the roads, parking lots and roadside campgrounds are much busier, especially in good weather.
Personally, I try to stay away that week, but it depends on your level of tolerence for noise and traffic. It's worse on the major routes - 112, 302, 3, 16 - so if you're on trails that run off the Kanc or Franconia Notch, for instance, dont be surprised if you can still hear the bikes an hour or two into your hike, depending on the winds.
But if you're after a "mountain experience", it might be a good time to go a little further out - Grafton Notch, Evans Notch, Mahoosics, Cabot, Waumbek, Great North Woods, etc. That's what I do anyway.