Oh, it will help, but only for a very short amount of time. Those metals will get pretty hot, the expanding steam will make the water splash out of the bucket and the rest of it will evaporate quickly. The fire will only stop, if the battery reaches a temperature of about 70°C (158°F). For that you need a lot of cooling material.
Yesterday in the news was a fire of a Tesla car battery, needing 36.000 gallons of water to extinguish it. They had to use two hose (the big ones) for over one hour to have it under control.
So if you put a small battery in a pool, then you are safe, I absolutely agree. I only criticize the wrong assumption that a bucket of salt water is the „only safe way“ to handle a battery.