Personally I would forget working as an airline piot in the USA unless you marry a local chcik, there nay be exceptions to that, but as mentioned above there is no shortage of pilots in the States at the moment.
You can use the FAA ATP almost anywhere in the world and has nothing to do with being a national of the USA. Let's say you were fortunate enough to be employed with say Cathay for example, then they would arrange evrything you need to live and work in Hong Kong, I would imagine most other carriers in different countries would be the same, ie, Singapore, China, Emirates etc...plenty Brit's working for all of those companies with FAA and or JAR licences.
However, without lot's of jet/turboprop experience then you will be very lucky to gain employment with those big carriers based on an ICAO ATP and low hours on light aircraft. Nothing is impossible though...