Yes. Women like to be associated with something that can make them feel proud for associating themselves with men. It could be status, money, or intelligence. It helps reassure their relationship with the said person, reassure they chose the right person by getting attention and positive remarks from other people, and they are seen as more important via association if the bragging is about status or money.
Women do this with their own family too. Men to do a certain extent as well. If their sons and daughters graduate from college or do something great, they will brag to anyone that will listen. In this case it's just about being a proud mother and to let people know that she raised a good son or daughter. Makes them look like a good mother.
Nothing really wrong with bragging about your sons and daughters as long as you not trying to rub something in another person's face who may have a son or daughter that's not doing so good.