Is Charisma a realistic stat?

I just listened at a documentary on the radio.

Someone checked out how others reacted towards him depending on how he was dressed.

Dressed, just that.



People reacted very different depending on if he were a costume or a hoddie.



This made me wonder if "Charisma" really is important for rpgs, as it easily may be trumped by clothing.

Is Charisma a realistic stat?