Can a preheater save fuel overall? (skipping the cold run phase)

Hello together, The heater in my “new” used (125kW diesel) can heat and air, i.e. heat cooling water or heat only the interior. If the cooling water is heated up, the engine practically skips the cold running phase, in which a lot of fuel is consumed. Is it possible that by heating the cooling water with the help of the heater and thus skipping the cold running phase in total less diesel is consumed than without the heating and heating up n of the engine from its own power loss?