Dont think the US Military has ever used a sawed off shotgun not even in WW1. The JSCS weapon in current use isn't short either at 470MM barrel length. Winchester Model 1897 pump shotgun was used in WW1 but it wasn't shortbarreled. It was even fitted with a bayonet mount.
A friend of mine carried a sawed off shotgun as a Marine in Vietnam. I have seen pictures of soldiers in Iraq with sawed off shotguns. These days they are outfitted with folding stocks, lights and other tactical goodies but they are still sawed off shotguns.
Let's define "sawed off." Current law says a shotgun barrel must be at least 18" long or it's illegal. Federal LE agencies regularly use shotguns with 14" barrels.
If by "sawed off" you mean ten inches or less, which I have seen, then they are just about useless. If by "sawed off" you simply mean shorter than the federally mandated 18", that's an altogether different beast. A 14" shotgun can be mighty handy for home defense.