With that kind of control, they could just put a gun to anyone's head and ask them to start mining bitcoin and do it the way they want them to. It wouldn't have to depend on how many bitcoin miners are in China at the moment.
The gun in the head strategy works best when you're only asking your populace to do simple things. For complex, technical tasks, the usual response is "Oops, I can't concentrate while you've got a gun against my head", and then you can shoot them but that's not going to help your task get accomplished any quicker. (This is also why working conditions at say Google or Apple tend to be pretty good, and why Soviet scientists were treated relatively well even if the rest of the population wasn't.)