can a local join a national

[aephi alum]

Short answer: Yes, she can join a national.

There is an NPC rule that prohibits anyone who's been initiated into one NPC sorority from ever joining another, even if she deaffiliates from the first. I'm not sure what the rules might be for non-NPC national sororities. But the NPC rule doesn't extend to locals - you can pledge and even be initiated into a local, deaffiliate, and then join an NPC sorority.

However, if the local is a member of the college's Panhel, Panhel may have adopted a rule that you can't initiate into the local, deaffiliate, and join a national (in the spirit of the NPC rule).