I doubt that will ever happen. PayPal leverages an "immediate payment" process used mostly for buying merchandise. Making a reservation does not require immediate payment, thus the PayPal approach is not the same because no payment is required up to the cancellation deadline.
They already take most major credit and debit cards so it makes little sense for Marriott to use paypal, first of all the transaction fees are higher than what they have already negotiated with their merchant services provider. Most frequent travelers pay with a credit card to get miles/points or because they are using a company card; and most business travelers will rarely to never prepay for a hotel reservation. Quite frankly paypal only acts sort of like an online escrow agency which in my opinion is not suitable for this type of business (as you don't need an escrow) but more for average Joe transactions with another average Joe.