There was some use of copper sheeting to plate temporary fortifications as a means of reducing the ability to light it on fire with projectiles (drawbridges, gatehouse embattlements, etc), but only during the siege itself. However sheet metal would be thin and unlikely to stop any kind of significant projectile. As others have commented, this is either anecdotal history or referring to the use against common metal fixtures. In history siege engines rarely decided sieges, they were weapons of reducing fixed defenses and terrorizing your enemy to move them into a position of surrender. Most sieges that were not surrenders were won by betrayals with someone opening a gate or lowering a rope, not the Hollywood drama of the besiegers knocking a hole and gaining the wall.