Do girls like "James Dean" awkward guys?

Do any girls like that type of guy? Really great looking but seriously disturbed upstairs? I'm curious because girls are always really flirty with me, but it never goes anywhere because of my "James Dean" social awkwardness. And unfortunately I'm shyer than him, so I never make the move. If I were to be more outgoing, are girls into guys like that, or am I screwed when they look past the delicious shell to see the nutty headcase inside of the candy bar that I am?