In theory, yes. In reality, apparently not. Most people seem to prefer to pretend to be something greater than they are in real life. Few prefer to create a mirror of the deficiencies and weaknesses they embody in reality within a game.But to have social interactions, a character doesn't need to be powerful. Playing a weak character can be fun as well, can't it?
EDIT:
For example, a nerd would rather fantasize about being a nerd with powers rather than the nerd he is that gets bullied at recess.
A dumb jock would rather fantasize about being a jock with brains rather than the jock he is who can't spell athlete.