Yes they’ll use more fuel than running on all engines. They always load the extra fuel that would be required for the maximum flight time with an engine out.

The extra fuel burn is due to the drag from pushing a non-working engine through the air, and from the rudder deflection to counteract the unequal thrust. It’s less of an issue on a four engine aircraft with a single engine out as they can increase thrust on the remaining engine on the side with the engine out.

Extra fuel burn is also required because a twin engine aircraft with an engine out can’t maintain the normal cruising altitude, and the higher you are the more efficient the engines are.

Thrust can’t be reduced much to save fuel because the speed margins at altitude are quite narrow - if they reduce thrust and therefore airspeed they’ll descend.