DeanP,
it all depends on how badly they need instructors at the time you finish the course, and it's the same with every school, be it in the US or Europe.
If you can afford it I suggest you take 1-2 weeks and visit some of those schools that can potentially hire you after completing the FAA instructor training. Take a thorough look before you commit because some schools are aware of the difficult situation in Europe and they may try to get advantage, give you the FAA training but no job offer afterwards (and you may end up with a "not-very-useful" FAA license).
Cheers / Pablo