Yeah, it depends on how early it is, the earlier you get it in, the longer you're going to have to wait for an interview invite. I'd suspect that the first big round of interview invites for most schools will go out in the next month or so. Some schools though, like Pitt, do interviews later than others, so it will probably be another 2 months or so until you might get one in that case.
If you apply later - after the big batches - you can usually expect to hear back sooner. I applied in November and got 2 interview invites within 2 weeks of the schools getting my apps. Of course, it's much better to be earlier, as you've got a greater chance of actually getting an invite.