Yep, what he said....

I think it’s very unlikely that you'd be required to surrender your FAA certificates; it's just that working for a foreign airline you wouldn't get to actively use them very much. Generally speaking, if you work for a foreign carrier you will operate their aircraft under their foreign govt issued air ops cert, and with an appropriate foreign govt issued pilot cert/license, and comply with the foreign rules/regulations of the country that the foreign airline is primarily based in.

Now, if a foreign carrier happens to have FAA registered aircraft on its books, it may be permissible to act as PIC using an FAA issued ATP cert, under certain conditions and in compliance with the provisions outlined in the company’s ops manual, if specified. Eg. Ferry flight of a newly acquired aircraft from the US back to the home base of the foreign carrier. That's about the only instance that I can think of that you might be able to excercise the privellages of your FAA cert while still flying for a foreign carrier.