We've had male advisors, so obviously you don't need to be an initiated sister.
Many of our chapters are 1) at colleges where there is nothing in the town but the college - so unless you're a prof there aren't a lot of college grads living there, and 2) many of these colleges require the main advisor to be a faculty member. So if we held ourselves to initiated sisters only, we would be SOL.
Obviously they cannot attend rush or ritual if they're not sisters.