The Diverge is a nice bike. It's on my list to look at seriously, if only a bike shop would stock my size and open so I can take a test ride. From what I've seen (too small for me to ride, though), it looks like it could be a great choice for bad road surfaces (or dirt or gravel, not that there's too much around here -- except for road construction!). It may suffice for your needs, or maybe not.
First, when you "become consumed with spontaneity or boredome take it all the way across the US," how are you going to do it? If you're going to throw a change of clothes and some rain gear in a small bag, and plan on sleeping in motels or B&Bs, the Diverge will probably be a great choice.
Second, what route are you going to take? Are you going to seek out steep and scenic mountain roads? If you're fresh and lightly loaded, you can probably ride the Diverge up reasonably graded roads.
The downsides are mostly gearing and load carrying. In the Appalachians, and the Ozarks to an extent, I made good use of a 20 gear inch low -- and walked a fair bit when it was too steep for that. The DIverge gives up two low gears compared to my touring bike 20 gear inch. As it's been said, what you don't have in your legs you'll need to have in your gears. I'll add that gets worse when you're tired from a long day's ride or fatigued from many consecutive days of riding.
For load carrying, I've used the traditional two racks and four panniers setup. That would be difficult with the Diverge. If you're going to be packing a sleeping bag, cooking gear, food, tent, on top of the minimum cool weather clothes, rain gear, and water, you'll either have to assemble a bikepacking setup, with ultralight gear and funky packs; or put everything into two enormous rear panniers which will affect your weight balance; or perhaps pull a trailer with the load. All of those are possible, but I don't have experience with any of the alternatives.