Not really. And simply because we're given no definitive reasoning for the scars. The scars could have drove him nuts(like a drop into a chemical bath), but we don't know. Equally, he could have been insane and given himself the scars because he thought they looked pretty.
Guard is right, the makeup and scars might possibly hold a significance to this Joker. But those elements don't hold a significance in this film, they're simply there with no explanation. I look at it this way, the comic book Joker is a guy who became insane and completely nuts after an accidental skin disfigure. The Dark Knight Joker is an insane maniac whose scars may or may not hold a significance to his insanity.
By not giving any explanations as to how or why this man is here, Nolan has created the most mysterious Joker to date. It would be nearly impossible to analyze that man.