Depends on how strong of an applicant you are...good stats will probably get you one of the first interview invites and give you time to prepare before interviews start (as well as more flexible interview dates to choose). Borderline candidates might have to wait until other applicants decline interview slots, sometimes days or weeks before the actually interview date.
Regardless, I wouldn't worry too much. At least in my experience, programs are pretty understanding of these situations. Most have "backup" interview dates when problems arise.