I doubt you will find out until the last week of July no matter how early you apply.
First, thanks for the responses.
Second, I am not sure which school it is because I am not back at my apartment (have everything laid out there). Only the application portion is due May 1, not the entire file (LOR, transcripts, certification, etc.). Two schools are due June 30 or July 1 for the entire thing (application included). On the application, it asks the other schools to which I am applying. Does it look better to say "none" (not a lie, but consciously decide to only apply to one)? When I sign the application, I am essentially saying that everything on it is true. What if I think that is the only one I want to apply to, then change my mind later?
I am not worried about when I hear back. I was concerned with the process: rolling admissions or simply admit/reject. I figured that the sooner I get my application in the better, but since my file won't be completed until later I guess it won't really matter.