An easa license allows you to fly any EASA reg. There are thousands of ICAO license holders flying in European airspace everyday.
knowledge is what matters in my opinion
not in mine, its networking, mates and luck unless your on a cadet scheme.
Part of that luck is your CV not going straight in the bucket before people have read past your training history. If it goes into the bucket at the training history that's just bad choice of training method/school.
And BTW I do that with all integrated CV's from the big british three so again it doesn't work quite the way you think it does.
But anyway wannbies always know best, and as its your money I have no problem at all you spending it how you like.