No. Pay With My Refund can only deduct your TurboTax fees from your federal refund.
This means you won't be able to use Pay With My Refund as a payment method if you don't have a federal refund, or if your federal refund is not enough to cover your TurboTax fees plus the fees, if any, for Pay With My Refund.
You can use Pay With My Refund to pay your TurboTax state fees – you just can't deduct any TurboTax fees from your state refund.
Note: There may or may not be a charge for Pay With My Refund, depending on your situation and which add-ons you choose.