I was complete very early and am very glad I did so. However, many people apply a bit later, are complete sometime in September, and still get plenty of interviews. It's not ideal, but it can be done. It depends on how strong your app is. If you're on the weaker side, it's definitely better to apply early to have a shot at interviews.
Like others have said, make sure to submit your primary and indicate that you are waiting on test scores. Don't wait until you receive your scores to submit your app. Since you'll be applying a bit late, make sure to study hard and rock the MCAT.