I agree with the above. I sent my application off mid September, not because I think this will gain me any advantage, but because I wanted to focus on getting the best grades possible.
It also helped talking to admissions tutors at the Uni's I'm applying who seemed confident I would secure an offer (can't hurt to ask).
Having said this, having now studied a bit more in depth, even a month later I feel my ps could be stronger, but hey ho not to worry, just more to talk about at interview