Yes she does. Generation X did not form until Generation X 1 and Blink was dead by then. Phalanx Covenant served as a precursor to that. Banshee was not their teacher in that crossover; he was a senior X-man trying to save them. He took on a different role once they were turned over to him at the school
Blink can be considered an honorary member in the same way that Carol Danvers might be listed as an honorary X-man.