The answer to that can be considered complicated. Depending on your relationship you could be considered a fag hag or just a woman who wants to hang out with her gay friends.
First off, you need to understand what a fag hag is. Fag hag was coined by gay men and is used to describe a woman who surrounds herself with gay and bisexual men, either as friends or as love interests with clear or unknowing knowledge that the man is gay or bisexual. Normally, the women who are classified as fag hags are using the flamboyant men in their lives to substitute a heterosexual relationship. Most likely, those types of relationships in their lives have failed and they want to have something positive and seemingly real in that part of their lives. This is a form of safety for both parties.
Do they really exists? I am going to let you be the judge. Do you know any stories of real fag hags? What about the women who married a gay man and then years later have come to the realization that their husband is gay? Is there a difference between those women and women who just have numerous gay friends? Is there a lesbian equivalent?