From what we understand, PayPal Financing (aka Bill Me Later) works as another possible funding source for the buyer's checkout payment -- i.e., just as the buyer could choose to fund their payment from their PayPal account balance, credit card, bank account or eCheck, they could also choose Bill Me Later to finance their payment with PayPal. This is supported for checkouts using PayPal Payments Standard, Advanced, and Pro, all of which our cart supports.
Payment processors like PayPal act as a sort of "middleman", where the buyer actually pays PayPal, and then PayPal pays you. The part where the buyer pays PayPal is kept self-contained at PayPal's end, so that aspect of things is essentially invisible to you and us alike. Regardless of how the buyer chooses to fund/finance their payment, PayPal only informs us when they complete the buyer's checkout payment to you, so we can process the order for you.
Checkout payments financed by PayPal using Bill Me Later should work just the same as any other payment on PayPal's checkout site as far as our system is concerned, so our order processing and affiliate tracking for you should work just the same as well.