You will also be looking at a large fluctuation in relative humidity. Since the bathroom becomes very humid for short amounts of time, the cake won't have time to absorb the humidity produced during those times into its bowels. It will, however, absorb the water into its outermost layers. But because the RH will drop significantly, shortly thereafter, the outer layers of the cake will release what was absorbed. This will result in a cake that has aged differently from outer layers to inner. It will also have an outer layer that has been subjected to drastic changes in humidity (and probably temperature), which will result in improper aging, or so they say.
Nevertheless, it is an interesting experiment. Afterwards you can teach us all with your results.