I would think that if your stats are good enough for an auto interview and you applied early, then you would be one of the first interviews. When I was in undergrad, our medical schools admissions office came to talk to us. They explained that you are put into three categories. The A group would be auto interviews, and they are interviewed first. The B group that may have bad gpa and good MCAT, or vica versa are read by hand. This means that they will get their invites later in the season.
So being in the A group gives you "better chances" simply because there are more slots left. But this only applies to the schools that use an automated system. Some schools (like BU) read all apps by hand.