Yes, if you are carrying a balance, interest will stop accruing for that part of your balance on the day that the payment is posted. This happens because when you make a payment, your balance goes down, and the more days you have in the billing cycle with a lower balance, the lower your average daily balance calculation will be, and therefore the lower your accrued interest.
If you are not carrying a balance from the previous statement cycle, then you can avoid finance charges entirely by paying the balance from the last statement in full by that statement's due date. In this case, it doesn't matter when the payment is made, as long as it's by the due date.