ICAO license or not, there is no agreement on converting a FAA license in to a JAA/EASA license. You don't have to take my word for it, just call the UK CAA, or any other EASA country's CAA equivalent and ask.
I have no idea about the rules in the Middle East but considering that there are a lot of FAA licensed pilots there I presume it can be done, but probably given a validation rather than a full license...?
Good luck.
CP