I have seen it, and it wasn't pretty. After Hurricane Andrew hit Miami, the Guard was called to assist with aid, organize volunteer teams, guard supplies, and make an armed presence to reduce looting. IIRC, they were authorized to shoot looters. I remember seeing one NG member trying to stop a kid who was trying to take a TV set - when the kid bolted, the NG member ran after him and caught him, but having had no training in how to restrain a resisting unarmed looter, he ended up in a tussle on the ground with the guy, with his M-16 dangling on the asphalt. The 16-or-so-yr-old almost grabbed it from him in the strruggle - yikes!!!
NG were called out and patrolled the streets again after Katrina in New Orleans, Louisiana (NOLA). In fact, they still were patrolling the streets, a full year after the fact, when I went with a church group on a summer work trip. For that matter, I think parts of NOLA are still under martial law, with the right of habeas corpus suspended (I am aware of at least one individual who was held without charge for over a year, and was just released this past week).
Since 'Martial Law' means 'law under military rule', I would say that any time you call the Guard out for a policing action you are instituting martial law.