Probably not if your experience in China is irrelavant.

to your new position. In other words, the judgement they made to hire you was not influenced by your experience in China.

I run background check all the time. The outcome often only includes public records everyone can get access to. It is heard of that some big name databases are integrating overseas information into current system, I've never had such experience though.

If your experience really matters, they should have requested contact information from you. If not, probably you are OK.

Anyway, don't do that again. It really does not matter what you think, you shoud DO right.