From personal experience, unless you are REALLY late into the cycle (post mid-sept), I don't think it matters.
A friend of mine literally destroyed the DAT. We're talking 25 (or 26)AA and a 28PAT, etc, etc. I'm not near his scores and submitted at least two months after he did (my file was complete 9/6/11). Within a week I had four interviews. Almost made me feel as if my "incomplete" file was "flagged" and they were just waiting on the scores.
Anyway. As of now, we have the same # of interviews. I even have one from a school that he applied to and didn't get.
So, who knows really what the "right" when is, or what adcoms look for. The thing is, you do want to get it in early or on time, but not too late.
I think getting close to October is really late.
Some schools deadlines are in Sept, I think OSU is the 16th of Sept.