In short yes. In the college I did my access course at, we had lecturers regarding the application process and personal statement writing in the first two weeks. We were encouraged to start the process straight away. Although that didn't stop myself and other lazy students starting after the New Year, but I don't advise that as it pisses off the lecturers.
I would suggest you go out of your way to make a good impression from the start. Be the Hermione Granger of the class. The lecturers only have a short time to form an opinion about you for your reference.