How bad is it if I miss the priority deadline for transferring?

One of my documents was sent a few days after the Feb 5th deadline because my current school is huge and bureaucracy makes things like this very slow. I was told that applications submitted after the priority deadline are based on space availability. Everything else was submitted on time. My stats are also very good. 2250 SAT and 3.8 college GPA. Do people who submit after the deadline usually get rejected?