If you actually think that is anywhere near the thought process that goes on when you talk to a girl at the bar, you're missing the mark completely. I noticed a lot of people around here are extremely short on the concept of being in medical school helping in any way.
I'm not there yet, but in my opinion, it would affect the calculation by establishing that you're smart and you're going places, and hence, are slightly more desirable. It's not a huge deal, and it probably isn't going to make the difference if you're already struggling in social situations, but I don't understand how anyone could think it isn't a plus. And it sounds marginally more interesting than "I work for some big accounting/consulting/O&G/etc firm".
PS why on earth would you expect random girls at bars to know the ins and outs of medical training, education, and the trajectory of US healthcare? I mean, have you not seen the "quotes from less informed premeds" thread? And those people are actually interested in the field...