Sure; why not? If I can stream videos on that same network for entertainment, or play another online, multiplayer game, why not use UDP if it gives a better user experience? It's not like UDP transport of those bytes is significantly worse network-wise and certainly lighter weight than those other alternatives.
Huh, that's not what I would expect at all. If you are having custom network protocols anyway, why deal with all the overhead that even a subset of HTTP brings? You might as well make an entirely new protocol at that point.