No. "Someone with XX chromosomes" is a stupid definition of a woman. Unless there are abnormalities present, no one does a chromosome test to check if someone is male or female. The distinction between male and female humans is obvious just by examining them.

Why the fuck make things more complicated than they need to be? A woman is an adult female human. The distinction between male and female in humans is obvious from a physical examination so adding extraneous details about chromosomes is just complicating things unnecessarily. I suppose it's a good way to pretend "I'm so clever I know about chromosomes" or something of that vein though.