I don't think so. Bleach, which is nothing else but hypochlorite solution, is basic (with pH in the range of 12/13) yet is is a strong oxidizer - and to use it you don't have to add any acid. With pKa 7.5 at so high pH almost all hypochlorite is in dissociated form.
Well, though bleach is basic in solution, for classification conditions we use stoichiometry, not actual pH of the reactants, hence oxidation by bleach itself proceeds in neutral conditions. When we add acid, or base to the reaction, conditions are acidic or basic, respectively.
Sometimes reaction is hold up by an acid or a base formed during reaction, but even then we do not take into account the base or the acid added, since they are not at the left side of chemical equation.