Wash out? Sure, briefly. It happens with rifles as well. Even on a .223, a flashhider may help, but you still see a flash in the NV. With a sound suppressor, it captures virtually all of it, however.
Other drawbacks? No all NV gear is going to be rated for the recoil pulse of the shotgun. Check with the manufacturer before buying NV for a shotgun to see if they say their gear will handle it.
Otherwise, all the other benefits and shortcomings apply that you would get with using a rifle.