No.
This was explained pretty exhaustively back when the original tax credit was available.
Your withholdings have no impact whatsoever on your qualifying for the credit and to what degree you do so.
Withholdings are just pre-payment of how much tax you owe. When you file you will get to knock that pre-payment off what you owe- if the net result is negative you get a refund, if it's not you get a bill.
But it's the original "what you owe" before you pay any attention to withholding at all that matters to the credit- as long as what you owe is equal to or more than the credit amount you get the full credit. If for example what you owe (again BEFORE even considering withholding) was say exactly the amount of the full credit, then you'd get a refund of 100% of your withholdings, regardless of how much they were.