You can apply as soon as the application is released. For full-time programs (with Oct. R1 deadlines) the applications are usually released in July. I would think that your application will be released earlier (a quick phone call to the admissions office can give you the information). And, yes, I do think it improves your chances if you apply earlier! Keep in mind that your application isn't considered complete until all of your information is in (including scores and LORs). Some schools may say that it doesn't matter and that all applicants within a round are looked at the same, but, I do think it shows your desire/motivation/interest (as well as your ability to get yourself organized) if you get the application done on the early end!

Hope this helps!
Jessica