No. At least not in the U.S. refurbished site. You can use any payment there that you can use for other online purchases from Apple. You can verify that by going to the refurbished site, select an item to add it to the Bag and then scroll down:
During checkout, you may use any online payment method available on the Apple Store. Learn more about Apple Pay. PayPal, Apple Store Gift Cards, and financing options may not be available for all products. Some customers may qualify for other forms of payment; call 1-800-MY-APPLE for information. Learn more about Payment & Pricing(opens in a new window).