Yes, you don't need to pay if they offer you free check-in of your bag at the airport - they do it because they need to move carry-on luggage from the passenger cabin to cargo hold, so they will not ask for payment if this situation occurs.

For example on fully booked OS flight CPH-VIE in November they announced at the gate that they were looking for passengers to gate check carry-on luggage to final destination because there was not enough space in the overhead compartments in passenger cabin. My bag was checked in to VIE and AMM at the gate despite my ticket said 0PC