To explain my question I'll use an example: We all know that sodium displaces copper in a solution of its sulfate in the reaction:
$$\ce{2Na (s) + CuSO4 (aq) \rightarrow Na2SO4 (aq) + Cu (s)}$$
My question is why don't some of the water molecules present in the aqueous solution of $\ce{CuSO4}$ also react with the sodium (Na) to form sodium hydroxide and hydrogen ($\ce{NaOH + H2}$) along side this displacement reaction. Shouldn't at least a bit of NaOH be formed?
I would appreciate a comprehensive response that a high school sophomore (me) would understand. Thanks in advance.