could a woman with aspergers date men?

It depends entirely on the severity of her condition, how she meets men and what kinds of men she has met. When it comes to people with psychological abnormalities it's all about what kinds of people they meet. Some people can handle it better than others.

I see no reason why someone with Asperger's Syndrome should not be able to get a date and even find a life-long partner who would support him or her. Asperger's and other SpLDs may, unfortunately, make it difficult or impossible for someone to be suited to certain professions but, very often, while they may be useless at one thing, they can shine at others. I have just come from reading some very encouraging and informative articles on Dyspraxia, especially some written by a very competent and successful journalist who, herself, is dyspraxic. Really, almost any disorder can be accepted and worked around provided that the sufferer can be given the right encouragement and develop the self-confidence to believe that they CAN be a valuable member of society. Perhaps you or I could never be an actor, an accountant or a research scientist but that doesn't mean that we don't possess other very valuable skills and abilities which fit us very well for other professions!