Well it wouldn't be any old mine, it would be chosen in a way that deferentially impacts the operations of the company that you want to harm. Yeah, it's a negative sum game, but that's how threats usually work. Even though it might hurt their hand, people sometime punch other people if they're convinced that it'll hurt their target more than it hurts them.
Income disparity would also be part of the calculation:
1) If there are V people with W average income each willing to pay X% of their their income to support Y other people while they strike and forgo their income of Z, then maybe you get more disruption for your buck by targeting part of the supply chain in a country where wages are lower.
2) If you're looking to make your target look scummy, targeting a more direct dependency might not be the right thing. You'd want to be funding a strike that should've happened anyway if only the people could afford it, not one that isn't justified.
As for the "China does not look kindly" thing... don't get caught? We're disrupting here, of course we're going to upset people. That's the point.