Yes they can, in come cases.

Car auctions give roughly three days for you to pick up a vehicle before they begin hammering you with storage fees. Timing that payment with the arrival of the car carrier can be time consuming, as storage fees add up daily.

If storage fees are reasonable, usually within $100-200, a carrier can make the storage payment and add it to the Bill of Lading as a reimbursement. However this is up the carrier's discretion, as it is a courtesy and not a requirement for them to do so.

Also, If you owe various fees worth hundreds of dollars, a carrier may be able to pay that up for you as they may not have the extra funds or be concerned about the total amount due for delivery.