>>2669170Rei literally says at one point that she wants to be one with Shinji, so we know she has the desire to be close with someone. Despite being fucked in the head Rei is still a girl and it seems like she has the same wants and desires as most people.
I guess the difference with Rei is as a partner you would have to be more responsible, since she has had a harsh life. It would be easy just to hurt her more.