I'd go with her, though I'm not sure if my reasoning is correct. Either the pronoun is the object of the preposition as, or it is equivalent to "student" which is syntactically accusative. I don't know why there is the temptation to use "As she".
You're not as green as Me.
Your're not as green as I.
As is a preposition, isn't it? I guess it could be one of those weird in betweener words and some people are using it as a pseudo-verb of being.
I'm just always suspicious of people using nominative pronouns.
Oh, well if you are writing the sentence, why not "Any university would be lucky to have her as a student."