I've heard varying things. If you read the Iserson guide, he says that typically ratings of applicants go up as the season progresses. I certainly don't think it matters anywhere near as much as it could possibly matter for med school.
There are a couple of other factors that play a role too, including where you're applying/interviewing, the fact that it's Peds (and not ENT or Ortho) and that it's a mutual selection process.
Overall, given that the match gives the advantage to the applicants, any edge you'd gain or lose from interviewing at the right or wrong time is moderated by the fact that it's your decision. I imagine a large number of peds programs place highest priority on making sure they fill their spots. If you're an Ortho program that only has 5 positions to fill, that's a lot different situation than what faces even the most highly rated peds programs (eg CHOP takes 42 and Baylor/TCH has 40 interns each year). If you're a mid-level program, that issue probably becomes even bigger. So if you're not a prestige *****, and have different criteria other than name that matter to you when you apply, the ball might be even more firmly in your court.
