Yes, it would be inappropriate.
I'm thinking of this like a job interview. EVERYTHING you do and say could possibly affect your chances. For instance, if I were to get calls regarding a position in February from someone who had already been told that they'd hear back by a certain date (let's say, April 1), I'd take that as a sign the person either doesn't pay attention to instructions or is way too needy (IE, they wouldn't be a good independent worker and would seek a lot of extra input instead of following their directions).
It's one thing to make sure they have all your materials, but another to call and ask specifically about YOUR chances. Either they'll give a generic answer or it'll impact how they see you as a candidate. Neither option gives you what you're looking for.