In all states, a shotgun concealed under a coat is a concealed weapon.
Even in states with a CCW law, those laws almost always are limited to handguns.
In general the only people carrying shotguns under trench coats are 211 (Armed Robbery) suspects, and they tend to get either shot or have their faces pushed into the concrete just prior to being handcuffed.
In other words, people with shotguns under the coat are considered by all to be Bad Guys, up to no good.