From my experience not right away. I am hoping to see a change in my scores this month and I paid off my cards mid january. I think it depends on when in the billing cycle you make the payment and when they report changes.
Your CRs will update when the CC reports the new balance. Typically, most CCs report at or around your statement date. The score increase would depend on your utilization prior to the paydown in comparison to the ending result.
