Do early applications ACTUALLY get an advantage?

I've read Paul Graham's post about how they would like applications to be sent in earlier, and how they would begin reviewing apps earlier and "interacting" with applicants. And thus, those who send in their apps early get an "advantage". But is this actually true? I mean, theres no real incentive, only a promise that by making their lives easier, we increase our chances somehow. I know in psychology, the lastest impressions are the strongest. If your a strong applicant and you apply 2 weeks before the deadline, your impression diminishes as other stronger applications come in. Whereas if you apply last minute with a large lump of applicants, you don't necessarily lose impact, your just one of the bunch. Some would argue that by applying early, you're on their mind longer and get some sort of benefit that way. But I'm not sure thats true. I think an interesting study would be to look at applicants submission dates, and compare those who got interviews / accepted against one another. My hypothesis is that a majority of those that made it in had last second submissions. Might provide for some interesting economics. (On that note, anyone ever read Freakonomics?)