I don't even think it's weird to ask, never mind inappropriate, especially if you've been in-contact! Definitely email them.
My cousin applied to a program with rolling admission and called to ask what the weaknesses in her application were. They said nothing, really, and that she should just apply earlier the next year. With that advice, she got into the program the year following!
But even if your situation's different, it probably can't hurt to ask, and it can be a huge source of relief when you get an informed second opinion about your application!