How important is turning in your application early?

I finish my semester at the beginning of May and I'm studying O-chem, Microbiology, and Physics. I was planning on taking the DAT mid May so that I get my scores back in the beginning of June and can turn in my application right at the beginning of the cycle. If I wanted a little more time to study and get volunteer/shadowing in, would it be significantly less advantageous to turn in my application mid-July or August instead? Thanks
Source: Student Doctor Network - Category: Universities & Medical Training Authors: Source Type: forums