Regarding an American traveling to China - I think you're still beholden to the host country's laws, no? You can't break their local laws just because you're from out of town.
Not to mention the punitive actions CCP could take against Tesla (as they try to build out a business there) to put pressure on SpaceX to stop allowing Starlink access in China. That wouldn't be fair either, but Musk is CEO of both organizations and I'm not sure the CCP would distinguish them separately.
I think this is pretty likely.
In the US the FCC has a whole set of systems designed to locate interference sources [1], and I've heard stories that they're extremely good at it. They even have a whole facility in Maryland dedicated to satellite monitoring!
[1] https://www.fcc.gov/over-air-spectrum-observation-capabiliti...
But I mean once a Chinese citizen gets their hands on the equipment, I'm not sure how China would stop them. I suppose they could have roving bands of listening posts looking for the uplink signals.
I'm sure someone could figure out a way to take payments for them. Many rich Chinese citizens already have bank accounts outside of China.