It will run the gamut from country roads to state highways to U.S. highways. And as noted, some wider roads, including interstates, can be safe. In some cases, the small country rodes can pose their own problems. For example, when I did the NT, a woman in Indiana warned us about yahoos running stop signs at intersections in the backroads that cut through cornfields. Two years ago I did the section of the NT from Glacier N.P. to Eureka, MT. There was heavy traffic in Columbia Falls, but very little on most of the parts of U.S. 93 that we rode except leaving Whitefish and entering Eureka, and the part of 93 that we were on had enough shoulder to get by.
One tip is to not take "shortcuts." You may see a more direct route than the one show on the AC map. One probable reason for the less direct route is potential traffic on the more direct route. For example, heading west out of Sandpoint, ID, you could take U.S. 2 instead of following the official route that crosses the lake and meanders along the other side of the river before eventually getting to the same place, but you might get squashed by a logging truck trying to do so.
In sum, t's completely doable even with the areas of moderate to heavy traffic. And at some point you will want to spend omse time in more populated areas. Meeting the locals is part of the experience.