Drain battery, yes. Damage, I do not know but doubt it.

I use a loose golf ball size wad of steel wool on the rare occasions I use it as a fire starter. It burns itself out quickly, just make sure you put it down on a fire-proof surface -or just into the fire.

You will see the steel wool begin to glow orange-red and shrivel up as it "burns" right away. the orange-red is like filaments in old tube transistors or electric heater elements. Try it once and you will get it right away [do not hold the steel wool when you try this].