Kenneth,
Without more information and photos of the weapon as well as ordnance returns of his unit, it is impossible to say. With more information, perhaps you may be able to get closer to the truth.
It is at least conceivble that this shotgun may have been used by your g.g. uncle in the war, as the 11th and 17th Arkansas Infantry were consolidated during the war and served as mounted infantry for a time.
It is just as likely, if not more so, that the shotgun could have been a prewar or postwar possession of your ancestor's, and may not have ever been used by him in the war.
Mike