Is it possible to fit full coverage fenders on a road bicycle with V-brakes?
It would help if you clarified what you mean by "road bike", since I've never seen a road bike with V-brakes. "Road bikes" are what many people would call "racing bikes" and they come with either disc brakes or caliper rim brakes; bikes with V-brakes tend to be either mountain bikes or hybrid/city bikes.

Nonetheless, it's perfectly possible to fit full fenders to a caliper-braked (or disc-braked) road bike, and also to a bike with V-brakes. Many road bikes don't come with the mounting bolt-holes for fenders but you can still fit fenders using other types of mount (e.g., clips or zip-tie-like straps around the forks).