If you are on a server (Tested with a localhost server), the client side attack cooldown will not refresh while your game is paused. If you hold left click and pause, it will look to other players as if the block is being broken (This visual effect will stop once the final block breaking stage is reached). And if you punch and immediately pause, the cooldown will still appear to be there for you when you unpause, even though server-side it's long gone.