If I live in the US, register a name trademarked in the US, but do it on a foreign registrar where the name is not trademarked, can anything happen to me?
Depends on what international treaties the country has signed and how seriously they enforce them. In any case, just because you're safe for now it doesn't mean you'll be safe forever.
I'm sure that ICANN (Which is primarily, if not under total) US control will force a hand over. The registrar I don't think has anything to do with it, it's basically the central registry that will assess said trademark. (If of course, by registrar you mean Domain Registrar).
If we're talking about a .com domain name, it doesn't matter where you reg it. Why? 1. If you're in the US, a party who can demonstrate TM rights to the term can use ACPA (just google it) to sue for ownership and up to $100K per domain. Or for convenience, use UDRP (again, just google it) and get control if they win all 3 counts. 2. Even if you're not in the US, the party can still use UDRP or ACPA and just get the domain name. The .com Registry is in Herndon, Virginia after all. Whatever method the party opts to use, they just have to serve notice to the registrar and they'll comply after verification.
Regardless of what CAN happen due to rulings by UDRP and ACPA the fact is that even these two authorities have a set of rules and guidelines to follow. They either have to have respect or pretend to have respect for Chinese commerce law when it comes to trademarks and domain name disputes. Even thought the internet is primarily controlled by the US all the authorities must have a code of behavior that they follow, with at least some semblance of fair play. Otherwise China would simply declare them an illegal outlaw entity! Think about it...if they have to be accepted by china as even semi legitimate entities then they would have to offer china some guarantees of fair play and probably the most important guarantee would be giving legal recognition to Chinese trademark and patent law lol.