Could a safe water ocean exist on a world with predominantly chlorine atmosphere?
Chlorine gas is dissolved in drinking water at low concentrations for disinfection purposes.  Chlorine gas has also be dissolved in somewhat higher concentrations in swimming pools.  

The amount of chlorine dissolved will strongly depend upon pressure.  If the atmospheric pressure on the planet is low the concentration of chlorine gas in the water will be low.  

Yes, most of the dissolved chlorine will reversibly react to form HCl and HOCl.  

For quantitative information about the equilibrium constant and solubility as a function of pressure and temperature see Solubility of Chlorine in Water Industrial and Engineering Chemistry vol. 33, pages 741–744.