Thinking about yesterday's post where I showed a police training video dealing with an attacker with a knife, I don't think concealed carry is a panacea for self defense. In the video, a cop has to have his hand on his gun and at least 21' of distance between himself and an attacker with a knife to have a good chance to survive. If your gun is concealed on your person, getting it out and using it effectively is going to take even longer.
I'd think that you'd have to be trained in both hand-to-hand combat and carry a concealed weapon to feel reasonably safe going in to bad situations. You'd also have to reflexively choose which to use in the split second things went bad.
Finally, if you want to see something really alarming, dig this.