I've only ridden on the section close to DC which has a fair amount of gravel over the dirt. Rode about 15 miles once with 28 mm tires & the rough ride gets fatiguing on wrists & butt after a while. There are some rocks & bumps, not really possible to avoid them all. The more rural parts may have less gravel but more mud. So it's probably doable but perhaps not too fun. Perhaps you could but some wider tires for the C & O? Re rain, yes it can get rainy in spring but OTOH this year was pretty dry & some of recent years also. Good luck.