That's a very good question.
The research we have shows that they don't apply as much, often because they don't think they're going to get it. Also issues that Dr. Konrad brought up in terms of unconscious bias often factor into the selection process inside the institution. Research has been done with two identical CVs, one with a woman's name and the other with a man's name. There have been completely different reactions to the same CV because of these unconscious biases.
Women don't apply as much, and there are these unconscious biases and other factors that influence the decisions in the end.