Assuming her personality matches her outfit (which is actually a big assumption...more on that in a moment), I wouldn't date a girl like that.
I do have tons of friends that would fit into your "weird" category, and honestly for the most part they are fairly normal once you get to know them. They look weird on the outside, and like the shock effect, but really they have same the basic needs and desires of any other woman.
Some of them have psycological problems and want the negative attention...those are the kinds I would stay away from.
I know one girl something like you described as her normal outfit.
A couple of her female friends helped her bleach the die out of her hair (she was a natural blonde so it looked relatively normal), took out all her extra piercings, did her hair nicely, and she put on makeup and a nice dress (it was for her prom), it took me like an hour to recognize her. She was gorgeous..lol.
She didn't have that many (visible) tattooes with the dress on and she looked and behaved like a perfect lady.
Kind of funny actually. But you know the old saying "don't judge a book by it's cover".