Do decomposition potentials change during electrolysis?

I was just wondering if decomposition potentials actually change during electrolysis. For example, if we reversed the Daniell cell reaction so that copper is oxidized, the half cell reactions would be:


$$\ce{Cu <=> Cu^2+ + 2e-} \qquad \pu{+0.34 V}$$
$$\ce{Zn^2+ + 2e- <=> Zn} \qquad \pu{-0.76 V}$$


if we assume both of the solutions are at $\pu{1 M}$ at $\pu{298.15 K}$, the decomposition voltage should be $\pu{1.1 V}$.


If we applied the voltage until half of the zinc cation solution reacted, we would have $\pu{1.5 M}$ $\ce{Cu^2+}$-solution and $\pu{0.5 M}$ $\ce{Zn^2+}$-solution, so that the resulting decomposition voltage should be higher:


$$E\_\ce{Cu} = 0.34 + \pu{0.0295 V}\times \log (1.5) = \pu{0.345 V},$$
$$E\_\ce{Zn} = -0.76 + \pu{0.0295 V}\times \log (0.5) = \pu{-0.769 V}$$


This should result in a decomposition voltage of $\pu{1.115 V}$ approx. Am I correct on that matter? I haven't found a single article that talks about the actual potential changes during electrolysis, even in my exam I only had to calculate the initial voltage, not what happens afterwards.


