No offers can be made before Oct 15 and I highly doubt that many schools do any interviewing before Labor Day. I do believe that electronic applications are making it easier for admission offices to skim the cream as applications arrive and push "the best" forward to be reviewed, etc which, over time, may make being "early" less of an advantage.
Either way, once those interview invitations go out that spot is gone and in many situations it is getting the interview that is the hardest part.