Of course not. If the way you ask people out on dates involves overt sexual advances, that's definitely not an appropriate way to do it in the workplace.
It's making an advance for the eventual goal of sex. How is that not a sexual advance? How is an email chain between interviewee and interviewer, discussing your interview results, not a professional setting?
People go to GREAT lengths for the "eventual goal of sex" all the time without it being labeled a sexual advance, including striking up what may seem like friendly conversation even though you may never have the slightest idea that their end game was actually to screw you (among many other things). Arguably the majority of anything that people do is for the eventual goal of sex.
The e-mail "later that evening" was not discussing the interview results. It was a later email, presumably on his own.
@pyrocat - You are making assumptions here that there was any quid pro quo involved. She was already rejected for the job. And then she was asked on a date. What was unethical and unprofessional was that he did it while being in a position of an interviewer.