Formation of O₂, Water, and Electricity from Hydroxide?
Yes, the overall reaction can be reversed.  The reverse reaction is called the oxygen evolution reaction or simply water oxidation.  Depending on the pH, you could write it as either

$$\ce{2 H2O -&gt; O2 + 4 H+ + 4e-}$$ or
$$\ce{4 OH- -&gt; O2 + 2 H2O + 4e-}$$

The reverse reaction happens when water is electrolyzed to make hydrogen at one electrode and oxygen at the other.  You may have seen that demo at one time or another -- here's a Youtube version.

Oxygen is a thermodynamically powerful oxidant, which is another way of saying that it is easily reduced.  This means that the water oxidation reaction requires energy input, about 1.23 V at the chemical reference state of pH 0.  But it usually takes even more energy to effectively reverse the reaction -- notice they used a 9 V battery in the Youtube demo, so about 8 of those volts are wasted in the demo.  Developing new electrode materials that can carry out the water oxidation reaction with less energy loss is a major area of fundamental research in chemistry today.

You also said the Clark electrode works with $\ce{H2O2}$ as an intermediate.  Depending on the details of the particular materials used, in the water oxidation reaction hydrogen peroxide may or may not be an intermediate.  Working out the fundamental reaction steps that happen at electrode surfaces can be very difficult.