Yes, most adcoms at about the 5,000th application just start shredding the rest for use at the Faculty New Year's Eve Party. I'm joking of course.
There is certainly some "structural" issues that make the odds slightly worse as there are finite interview slots and finite seats. However, even with rolling admissions, the schools spread their work and acceptance across the cycle. So are the odds of late app over early app against you? Yes. By how much? really hard to say, could be very little or more depending on the school.
The absolute answer is, it doesn't matter, You have submitted, you have no influence at this point to alter time, and things will happen as they happen. Speculating, hoping, worrying will do nothing but stress you out. This is actually the second stage of the recently proposed disorder for DSM-VI :
PREMED: Psychotic Reactionary Event Manifestation Exclusionary Disorder. This stage is known as
Application Submission Syndrome or ASS. People suffering from this malady have an overriding sense of powerlessness and cognitive dissonance with obsessively reviewing in minute detail of the their application and hypothetically projecting worries, scenarios, and other delusional thoughts based on rumor, innuendo, myth, and whatever other misinformation they may acquire. In short, they can make an ASS of themselves. There is no treatment that has any effectiveness as most suffering it have a temporary loss of rational reasoning. On occasion, these can lead to critical episodes which may require restraints and sedation. For further information on this see
PREMED: Psychotic Reactionary Event Manifestation Exclusionary Disorder
PISS: Post Interview Stress Syndrome
