No.  Making your credit card payments by the due date is what will affect your credit score.  There are no benefits associated with making early payments.  However, making your payment well before the due date on your credit card statement is a great habit to practice.  Waiting until the last minute to make your payment can sometimes cause it to be marked as late.  This can be attributed to the time it takes to process your payment as well as other factors.
The three things that most impact your credit score and that are most important to keep in mind are timeliness of your payments, the length of your relationships with your lenders and the percentage of the credit that’s been extended to you that you are using at any given time.