Yes, foreign pilots can be typed. Exactly as Freak said. My employer (a US regional airlines), sent me a "release of information" paper for the FBI (I'm still an Italian citizen).
An FAA is an ICAO license. Period. In order to work in other countries, such license must be either validated or converted. In some countries (ex. Emirates) it's an easy process, whereas in other (European countries) it' a BIG pain the the a$$.
The reason the FAA uses certificates instead of licenses is that certificates do NOT need to be reniewed.
PEACE