I have seen it work numerous times and have done it myself. It works for finding pipes, wires, water, etc. whether or not they are metal, plastic or other material. I always assumed it worked because of the slight disturbances in the magnetic field created when things like pipe or wire are buried and an unnatural void and break in the soil causes some sort of minute disruption.
Exactly right. The metal pipes and wires are influenced by the man-made submarine communication antennas - VLF. Also by nearby electrical current from nearby powerlines. The plastic pipes are probably the breaks in the soil where the remnant magnetization of the minerals in the soil are disturbed. I use fancy equipment to find both. (Utility locators work off the VLF, and a magnetometer to find disturbed soils. The mag doesn't always work.)
The groundwater issue might be due to self-potential or streaming-potential electrical forces caused by flowing water through the soils. (Pretty sure it needs soils, but perhaps it can also happen in plastic pipes, which may account for finding them).
Although I still am not sure how a wood stick is able to conduct the energy. Wire rods yes. Perhaps the wood has enough moisture in it. And it may be that it is more that the signal is picked up by the person (some with better receptors due to more iron, more free ions, etc.), and the wood stick or metal rod is just the indicator.