If we reformulate the utility function to include not only money but also bonds of various maturities (money and bonds in utility function), the zero short-term interest rate is not equivalent to the zero marginal utility of money, because there remains the arbitrage relationships with the longer maturity bonds with positive interest rates (Iwamura, Shiratsuka and Watanabe (2006)).
As long as the marginal utility of money remains positive, the “satiation of money holdings” will not emerge even though the zero bound on short-term interest rates appears in the economy. In this case, the increase of real money balance can affect the market interest rates, pushing down the forward rate relative to the future rate.