The US pilots' market is awash with pilots furloughed due to 9/11 and the subsequent Chapter 11 bankruptcies of several airlines, and collapse of others (most recently Independence Air). The US pilot unions are unlikely to look kindly on aliens attempting to get in on the market while many thousands of their members are out of work.
However, as previously metioned, the FAA ATP license [sic] is a recognised ICAO licence, and will be accepted by many, many countries for operation of aircraft on their national registers. For those countries that require a conversion to their national licence (Hong Kong was mentioned, but there are many others - including all of the EU), you are almost certainly theoretically required to meet all the medical requirements of an initial issue, but individual AMEs may be more lenient. You won't have a leg to stand on, though, if you're refused a licence on those grounds, so it would be as well to check first.
Scroggs