While an interesting hypothesis, it seems unlikely: one copy of each x-chromosome is deactivated in each cell, and this is done randomly in development.
This is one of the reasons women have superior colour vision to men so it's likely enough. Some women have two different types of red cones while men have a maximum of one. There are many other sex linked diseases as well. Unless an allele is fully dominant if it's on the X chromosome men will display hreater variance.