I know that Ohio responded with supplementals based on when VMCAS was submitted, but I didn't think it was rolling in the same sense that some med schools are. I don't think someone that submitted VMCAS in early September would get an interview invitation over someone with the same stats who submitted right at the deadline. They would get their supplemental sooner, but have the same chance of acceptance. At least that was the impression I got.
I submitted my application the evening before the noon deadline (Oct 1?)...I think. It was right around there, anyway. I had it sitting in my computer done for a while, but was too freaked out to submit it, in case I'd forgotten anything. I actually did remember a few honors/awards that I hadn't included in the first "draft" of it, so I'm glad I waited. I honestly didn't want to wait quite that long, but one of my rec letter people procrastinated, and then was impossible to get in touch with. It was quite frustrating. I know they don't have to be in until the 15th or something like it, but I didn't want to give up the ability to edit the eLoR section...just in case. It turned out to be a good decision, because on September 30th-ish, she called me to say that she couldn't find the email from VMCAS! I had to delete her from that section and re-submit her information so she'd get another email and could fill out the rec letter. Needless to say, I was a bit on edge that week.
This is a longwinded way of saying I recommend waiting for a little while, especially if you have a similar mindset as me, but not waiting so long that you're submitting it the morning it's due, because, as was mentioned earlier, it notoriously crashes at the last minute. And then you're screwed.