Gen or rep, I never travel internationally with more than 2 watches (one on wrist) and it's never an issue. There's actually a funny comment in the midweek wrist check since the pic I took is in an airport...not sure if that was a serious comment or not though.
Not sure about the EU, but on the occasion I've had to make an insurance claim on a package that went missing, I had to provide proof of value like a receipt. I've never ever gotten a receipt with a rep so that may be a little difficult to provide.