This paper is based on my contribution to a debate, organized by MPIDR, on the question displayed in the title above. I was asked to present arguments for the "yes"-response (together with Laurent Toulemon, and arguing against the "no"-side represented by Gerda Neyer and Dimiter Philipov). As pointed out in the paper, the most important theoretical reasoning relevant for this question is the gender equity theory. A number of studies provide sound empirical support to it, as discussed in the paper in details, and thereby also a rationale for a positive impact of increased gender equality on fertility.