The shares of many non-US companies, including several H shares (companies incorporated in the mainland but trading on the Hang Seng), trade on US exchanges via ADRs -- American Depositary Receipts. It's a bit of a stretch to put it this way, but ADRs are a bit like passthrough shares traded on the likes of BTCT.co: in the case of an ADR, a US financial institution holds the 'real' shares overseas and issues certificates (the ADRs) that trade on a US exchange. The underlying shares themselves are called American Depositary Shares (ADSs). This is how it works for shares of a single company, such as CHL (China Mobile), for example. (A bank can also issue certificates in more than one country, in which case they're called Global Depositary Receipts, or GDRs.)
Although it's ADRs rather than ETFs you'd be after if you wanted to trade shares of a single Chinese company on a US exchange, that doesn't at all address the part of your question about being denominated in a decentralized currency. For the 400,000 shares in ASICMINER themselves to become available for trading on any of the established exchanges, they would need to be registered appropriately and denominated in the currency of that exchange. IMHO, that seems unlikely.
Should Friedcat ever want to do it, though, I wonder about a reverse takeover -- a shortcut to an exchange listing, whereby a private company buys control of a listed company, and the private company's shareholders then exchange their shares for shares in the public company. (The most famous example of a reverse takeover was Buffett's taking control of Berkshire Hathaway.) Given Chinese restrictions on foreign investment, I imagine this could be a hornet's nest of complication and a potential disaster for non-Chinese shareholders.
