Yes, if your tax refund is eligible to be used you can pay for the TurboTax account fees with the federal tax refund.
Note - There is $39 service charge for this option which will also be paid from the federal tax refund.
See this TurboTax support FAQ for paying with the refund - https://ttlc.intuit.com/community/payments/help/can-i-pay-with-my-refund/00/25711
