An applicant who completes the application later in the year is less likely to be accepted. It gets more competitive as time progresses, but it's not impossible to get a seat. Schools wait-list new applicants when their seats fill, but it doesn't mean you won't get in. Students often apply to multiple schools, so when they choose a school, all of the other schools which accepted them open.
To ease your mind, I recommend you apply even if it is late in the year. First of all, you'll meet the faculty, see the schools, get a feel for interviews and, most importantly, get a chance to make an impression on a school. If you don't get in due to a wait-list, you'll be far more likely to get in the following year. In other words, no harm can come by applying late if you cannot apply early.
I applied in December or January, selected an interview date for March and was accepted. This was at OSU where there are only 64 slots. They slowly accept people until they fill around half of the class, then hold off until all of the applications are in before deciding on any more. If you need stats to compare this late acceptance to, I had a 3.4 and 330AA, 330TS.
Hope that helps. Good luck.
