Primary for concealed carry it would be too slow and clumsy for me, I'm not sure how much practice I would need to be able to draw something like that and hit my target in a hurry, I don't think I'd ever get close to what I can do with a normal sized handgun. Car carry, well maybe anything goes, I'd opt for a handgun caliber myself instead of a high pressure bottle neck round, but maybe you live in a special place? A 5.56 or 7.62 is going to fly a long ways and go through a neighborhood a long ways, so it doesn't sound so good to me, regular handgun calibers are hard enough to keep from going where you don't want them to go. I do understand having something more than a regular handgun for when your busted down in the middle of nowhere, I think I'd pick something in the way of a carbine for myself. In this state, I'd have to keep a carbine or shotgun in the trunk, but with a good handgun and a car that still runs, I should be able to get to the trunk without a problem to get that firepower.
For primary concealed carry on your person in the calibers those come in, and as clumsy as they would be, forget it.