The real question if an rich would date someone who is having less money then her, guys get rejected because of this far more then girls. Personally I don't care much for money, I would not date an girl who is taller then me, but I can date an girl who is richer then me, even though she may try to manipulate me with it, so it's having an advantages and disadvantages.
If you are asking me, then my answer is I have decided to stay single till death, so I am never going on a date.
However in general, yes why not, the woman being richer than man is not going to be a problem, the important point is her personality and her thought process. For example if the woman is very rich but at the same time is humble, soft hearted, also confident and is highly principled by nature then I am sure a man would not have any problem dating such a woman.
I don't care if she is richer or no.. in all cases i'm the man and i'm the dominant and i don't need her money , I'm the one who will control the house physically. So she has to adapt to my life if she really loves me whatever i'm rich or no.