Shouldn't matter
I'm not from the airlines any more, but do work biz jets now.
I remember from my days as a trainer that 'foreign ' JAA licences caused problems when it came to UK TRE's signing off a class or rating as often the DGAC (french) wouldn't accept it and alike, so the company I worked for insisted that all non UK pilots had to convert to a UK JAA licence and post transition it really wasn't a problem.
Not sure about the recruiting side of things. I don't see any reason why if you have already converted it to a UK issued licence it should even be considered as a problem.
Hope that helps.