Yes, provided you have no citizenship issues, then you can work with an FAA licence anywhere in the world provided you are operating an N registered aircraft or going somehwere where they can just issue you a 'local' licence when you show them your FAA one. I don't know how many jobs that there are like that out there but it is possible. The job market in Europe at the moment is actually pretty good - better than in the US so I understand.
You're right that if you do your CPL and IR in the US, provided it is a JAA syllabus and the school is approved then you will get issued a JAA CPL/IR - no need to convert it. I think you still have to do your IR test in Europe, so you can't do the whole lot over there but you can save money by doing most of the training there. I did my CPL in the US. The JAA training you do in the US will be done to the same set of standards that it would be in Europe and you will be examined to the same standards.
Hope that all helps - it is a bit of a minefield but you just need to choose where you plan to live and see what licence you need to work there.