If directionality and "diodes" exist in wire then I should be able to detect pulsating DC on the other end when connected incorrectly.
I don't think it will be a simple measurement like you would with discrete components. These diodes, if they exist as has been claimed, are distributed in the body of the metal in a way that are not as simple as we could call "series", "parallel" or so on as we would characterize discrete components. Whatever the effect of these diodes in the signal transmission, it will be elusive and difficult to capture.
Can it be measured? It's possible but to be honest, it may be as complicated as rocket science. As Richard Feynman said, if what he did could be explained he probably would not have received the Nobel prize. If directionality is easy to be measured, you probably would have seen someone done it already.
Just like dark matter, dark energy ... just because we have not seen it directly, it does not mean they may not exist.