Initially I would have thought yes, but now I am not so sure, and it must depend on the school. It wasn't at first clear to me if my top choice school had rolling admissions or not - I was looking to see if there was some date before which applications for this next year would NOT be accepted, and I couldn't find anything, making me think it might have something along the lines of rolling admissions. So, I called and asked. The woman in the admissions office told me that I could submit an application this summer if I wanted to, but I probably wouldn't hear anything (even an acknowledgement) until at least January. Basically it sounded like they would start looking at all the applications at the same time.
What was less clear was if they would look at them in the order in which each application was completed. I have often heard that it's best to apply early because if you apply later on all the spots may have been filled (the admissions decisions may not have been sent out, but as far as the school is concerned the spots have been filled.) I don't know how true this is, and I'm sure it really depends on the school.... do they go along through the pile, making firm decisions as they go, or do they wait until every application has been looked at before making a firm decision? That probably depends on the size of the program and how many applications they receive.
I'd call the school to find out how they do things. If they don't even look at applications until after the deadline, and then don't make decisions in the order in which the applications were received, then applying early probably doesn't give a leg up. Still, if you can apply early, it's nice to have one fewer thing to worry about. I plan to apply late August/early September.