they really only cared about one thing and that was your GPA. Which semester you applied for didn't have any bearing on you chances for admission. You could also attend during the summer as a "visiting student" without actually going through the admissions process, but they made it very clear that attending as a visiting student did not increase your chances for admission as a regular student, you were there for one semester and that was it.
I'd suggest you call and talk to someone in the admissions department. They are usually open about the admissions criteria.
And yeah, the name of the school does matter to some so be careful with that, especially when talking or writing to school officials. 🙂