If you're talking about telling the professor where you applied, the only downside may be if you only applied to ivy leagues because they're ivy leagues and not based on research interest (mainly PhD focused). Kind of shows if you have a focused interest or if you're just applying to apply type of thing.
I had this happen to me too. I've been told that this is to see if you applied to random schools or if you have an actual idea of your research interests.
I'm assuming that I should give up on Drexel at this point. I'm still waiting post interview(which was 6 weeks ago) and I've been checking the application website everyday. Anyone else in the same boat?