Will TurboTax let me pay for filing of my taxes with my refund without me having to add my credit card info?

https://ttlc.intuit.com/community/charges-and-fees/help/why-can-t-i-deduct-my-turbotax-fees-from-my-refund/00/25621

If your refund is enough to cover your TurboTax fees PLUS the extra “refund processing” fee of $40 ($45 in CA) and your forms are ready then when you are in the FILE section you can choose to have your fees deducted from your federal refund by a third party bank, who will take out your fees and send you the rest of your refund after the IRS issues the refund. 

Please make note that if your refund takes too long to arrive (IRS delays, etc.) then you will also be agreeing that the TurboTax fees can be extracted from your bank account even before your refund is issued by the IRS.  This comes as an unpleasant shock to many people every year.  

 If you can possibly pay your fees upfront using a debit or credit card, it will save you that extra fee and even more importantly, the possible aggravation and delays that are often the result of poor handling/poor customer service by that third party bank.  We see way too many instances where refunds are delayed for months when users choose refund processing. There have been lots of complaints; there are a number of things that can go wrong when you use refund processing.  I suggest avoiding that situation if at all possible.  

And....you can never pay state tax due from a federal refund, so do not expect that.   The state tax due has to be paid directly to your state.

What is Refund Processing Service?

How can I see my TurboTax  fees?   

https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-account-billing/review-fees-turbotax-online/L1XnIzgzg_US_en_US?uid=m682vq7k