An overflow tank is usually not an integral part of the cooling system but the reservoir on your car is. Filling that reservoir fills the cooling system. Now, how much damage is done? What can you do? What should you do? I’ll throw a suggestion at you. Remove the splash guard and fill the reservoir with water and check the source of the leak. Very possibly it is the radiator end tank. If so you will want to know if the engine is damaged before attempting to repair the radiator. Post back the source of the leak.