You'll be walking up every hill and even every modest incline. But I don't see that as a problem. Plenty of people hike long-distances. The Pacific crest Trail, for example, is about 2700 miles. The American Discovery Trail runs from Atlantic to Pacific coasts and people have walked that. Pushing a bike uphill on a road is easier than carrying the same gear uphill on your back. And then when you get to the top of the hill, you climb back on the bike and off you go. Worst case, there is no level ground and you end up walking exactly half the time. But you still have a much easier time than backpackers, at least on roads. More realistically, you'll stick to the flatter parts of the country and walk the bike perhaps 20% of the time.
Compare yourself with pedestrians, not other bikers, much less motor vehicles.