This question goes into the very nature of the work function that the Kelvin Probe Force Microscope (KPFM) measures.
https://en.wikipedia.org/wiki/Kelvin_probe_force_microscope
Let's say, you have a battery of 1.5 V, you connect two identical metal leads to both ends. If you measure the work function on both ends with a KPFM, would they be the same or would the work function be different by 1.5 eV?
A co-worker and I were discussing this, and unfortunately, we don't have a KPFM to test this. The idea is that since the electrons have energies differing by 1.5 eV, there would be a difference in the workfunction between the two metals by 1.5 eV. I disagree with this, but cannot give a good argument why I think the workfunction for both leads would be the same.