Hey benchdaily,
This might differ from what most people think, but based on what I heard, most schools still process in the order it is received though they may say "we don't start processing until May." I recently applied to an away that said applying early doesn't have a benefit, but everyone who did that away at my medical school last year basically said that was only a half truth. In summary, applying early can't hurt, and almost always helps. If you can't get in touch with the coordinator, try an email and try to contact one of the registrar's staff and they should be able to transfer you or also assist with the questions you may have.