No, I think she knows what she looks like but, to be candid, the type of guys she ends up with is pretty unrealistic. It's not like she's a particularly charming character, personality wise, either.
I don't really have an opinion of Lena Dunham - I haven't read any of her pieces or commentary - I've seen Girls, which I think is great, but only because I see it as a pretty funny indictment of Millenial values (which may, or may not be the point).
I'm not sure if she's like Hannah, or if Hannah is just an over-exaggerated version of her foibles, but I don't really care. I have no interest in her opinion on things, to be honest.