If you convert to a JAA/EASA license then you will be treated the same as a "thoroughbred".

The main issue you will have is the language barrier. For most airlines in Europe, you'll need to speak the local language.

An advantage of having the JAA license is that many airlines in Africa, Asia and and the Middle East base their licensing system on the JAA system, so they often favour pilots with a JAA license over an FAA license.

The 'underground networks' in European airlines do exist, but their 'power' is in decline as Human Resources departments have increasing amounts of control over the entire recruitment process. Most pilots I know who got jobs for European airlines did so through the normal application process.