It does and you can quantitatively calculate the amount of the peak shift using Nernst Equation if the kinetics of the redox reaction(s) is/are fast (or the reaction(s) is/are reversible).
It hard to judge and should vary case by case. If increasing the molarity of the metal oxide results in changing the electronic structure, morphology or chemical composition, the redox peaks' position will be modified. I suggest you trying it experimentally.