i sent in my apps very late, mid March. i have called several times to make sure my apps don't fall into the cracks. usually, the person that picks up the phone has no clue what is going on, they are probably a student or something like that.
but by calling, i finally got the assistant dean and got some answers. you believe it, he even calls me back and leaves messages if I get his VM.
i think to call is no problem. just understand that they are very busy and that it may take several calls to get a honest answer.