[hwillis]

A wire will cause the air around it to assume the same potential, ie the same as air that is low to the ground. If you are 6" above the top of the wire, the voltage to ground will be the same as 6" above the ground. Note that the wire could be made of anything even slightly conductive, because it just needs to be ~10x better than air. The plant already causes the potential to be zeroed out, just like a human body: https://www.feynmanlectures.caltech.edu/II_09.html

Using copper allows you to absorb low frequency radiation like FM radio. Note that you aren't blocking it to any significant degree, since it's just one wire and not a cage. It also isn't causing any voltage on the plant since it's just being absorbed by the wire.

[tengbretson]

The plant will zero out the potential, presumably because there is a small current through the plant itself. In the presence of a nearby antenna/grounding rod the current through the plant would be significantly lower, since there is a less resistive path to ground.

In the case of my hypothesis, the mechanism I'm describing would likely be somehow tied to the plant's perception of that current.

[hwillis]

It's in the range of femtoamps. Current in general is not really very directly measurable, particularly for biology. Instead you do things like measuring voltage across something or magnetic fields.