At this point in my life, as a crossdresser, I don't think I could ever date a woman again who didn't know very early on about 'Caroline' if not, preferably, before the first date even. I'm just too out there, and my social life is very intertwined with my CD life. It would be next to impossible for me to hide.
Very recently, I did have a date for the first time 'as Caroline' with a woman who knew about me before hand and even met me for the first time as Caroline, and I'd have to say, I think it went off very well. It helped that the woman was accepting, and already a bit versed in the crossdressing community. I didn't really approach it any differently than any other date. It was mostly conversation and a some dancing. The way I was dressed did offer a lot of conversation points however. She commented on everything from my jewelry to my corset so that made it rather interesting.
So to answer the question. Yes. I would date a woman as my femme self. Indeed I already have, and I'd be more than happy to do it again.