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From the FAQ's they only state that the card has to be in your name when you are picking up the car

We accept all major credit cards, including American Express, Discover/Novus, MasterCard, and Visa. Debit cards branded with the Visa or MasterCard logo are also valid forms of payment. Credit card information cannot be changed once the purchase is complete.

Please note that you do not have to present the same card to the rental counter that you entered into our website when making the reservation. You may use a different card at the counter, as long as it is in the primary driver's name. If you plan to use a debit card when picking up your vehicle, you may be required to provide round-trip flight information at the rental counter.

Though it may depend on which type of car rental (traditional or name your own price) you are talking about. A message to Priceline Customer Service would probably clear it up quickly.

The charges will again depend on the type of rental. If it's a name your own price, they will charge the full rental when the offer is accepted. If it's a traditional rental, they will swipe the card at pickup, put a hold on the card for the rental amount and the deposit (for a normal car somewhere around $300) and release the deposit when the car is returned. The amount of the hold depends on location and type of car.

I think it would be much less confusing for you to just pay for it all and get reimbursed from them.