Narcissa prefers to protect her family above all else. u could say she is Gray. Whem Draco took the Dark Mark and was ordered to kill Dumbledore, she appealed to Snape to protect him. In the Forbidden Forest, she willingly lied to Voldemort when Harry zei Draco was alive.
I don't know why. Maybe they're sexist. But then again, Bellatrix was a death eater. Maybe Narcissa just didn't meet the death eater standard. But she was a big supported of Voldemort, of Lucius and blood purity. She does address Voldemort formally, as the 'Dark lord' a chooses to believe in them. That is, until Draco's life is put in danger- and then she sort of does a complete 180 to ensure her sons safety. A bit like Lily, yeah? Plus, she did lie to Voldemort about Harry being dead. Sooo no, not a death eater.