I was accepted to NYU last year and had to ask them to postpone the deadline for the deposit for me because I wasn't in the country. They were fine with it. I paid them about two weeks after the deadline. I don't think they thought it was a big deal.
I applied about a week ago. The waiting is killing me, haha. However, when I was applying so late they told me to finish up my application by the end of January. So, maybe they will decide soon?