The ME training will carry over but you are required to sit a flight test to get it added to a UK/JAA licence as it is a Class Rating not differences training.
Al, you also need to re read the question, the poster has a JAA licence with a based on FAA licence and wants to get some differences training and want's to know if it can be applied to his JAA licence.
I was posting the second bit for the benefit of other readers, as there seems to always be confusion between RATINGS and ENDORSEMENTS
As an example, I have no JAA MEP rating on my JAA PPL, but I can still fly MEPs in the UK thanks to my FAA ME(note: no P) rating. So in effect it does carry over, especially if the FAA Cert is based upon a JAA cert....