Irreversible chemical reaction in a battery
The original poster has a serious misconception by equating a reversible chemical reaction with a reaction that is in equilibrium. The electrochemical reaction that allows the battery to deliver energy to the load (such as the copper/zinc reaction mentioned) is always reversible in theory by reversing the current flow. However in addition to the electrochemical reaction, there are other chemical reactions going on inside the battery which are not reversible as well as geometrical changes that may not allow the reactants to be close enough for the electrochemical reaction to run in reverse. In batteries designed to be recharged, these geometrical and irreversible chemical changes are minimized to allow as many recharge cycles as possible. Batteries not designed to be recharged therefore usually can't be recharged fully and have very few recharge cycles not to mention a high probability of gaseous or corrosive liquid leakage.

At equilibrium, both forward and reverse reactions are going at the same rate, but this is only discernable microscopically. At a macroscopic level you see nothing happening. So a battery is never at equilibrium while you are using it since at that point the battery is completely dead. Then (or preferably sooner) it is time to recharge the battery or throw it away.