You can begin turning in the ERAS application on September 1st. As for whether timing of the application matters, I would say no. If you have great numbers and will be getting lots of interview offers, I have heard of people being offered interviews in mid-October and there are even a few programs that have an interview towards the end of October. If you are going to be getting letters from your rotations in the fall, you are going to have to stay on their ass and make sure that they get them in quickly. Sometimes letter writers take a long time to get that letter out. With a November 1st deadline, it may make things a little tight.
Also, most programs don't look at your application until it is complete (board scores, trasncript, LORs, personal statement, common application form, etc), so I guess that if your letters won't be coming in until October, it won't really hurt you to wait to submit until then. This is not a first come first serve basis. Most programs don't begin offering the bulk of their interviews until after November 1st. However, theoretically, by submitting early it may show some eagerness and organization on your part which may look good, but that is just rumor that I have heard.
I hope that helps.