Irreversible chemical reaction in a battery

"In reversible reactions, as the reactants react with other reactants to form products, the products are reacting with other products to form reactants."
<http://chemwiki.ucdavis.edu/Physical_Chemistry/Equilibria/Chemical_Equilibria/Reversible_vs._Irreversible_Reactions>


Inside an ideal battery, the chemical reaction is reversible (at equilibrium), thus the oxydation-reduction reaction Zn + Cu2+ = Zn2+ + Cu is happening in both direction at the same rate right?


Now, for a real battery, there's resistivity inside it due to many factors, thus the chemical reaction is irreversible. My question is, during the irreversible reaction, is the reaction happening in both directions but at different rate due to resistivity inside the battery or it is just like the combustion reaction happening in one direction?


