The most likely consequence of this change is that there will gradually emerge a change in sex roles in our society. As women hold more such positions, authority will seem like less of an exclusively "masculine" quality and it will come to be seen as more natural for women to have power over men.
This might well continue a change that we are already seeing in sex roles within marriages and other such relationships. As the idea of women in power comes to be more accepted, it is likely that the idea of men staying home to take care of their families will become more acceptable as well.
The major impact of this change, then, is likely to be felt in the roles that we assign to the sexes in our society.