For anyone doubting whether Karl actually comes out with what he says, or whether it's scripted, I highly recommend you listen to his early days on XFM with Ricky and Steve.
Like has already been said, he was just their Producer in the Studio and didn't feature at all for a long time. Then one day they asked him something on air and he gave a ridiculous answer and it just grew from there, until he became part of the show.
Obviously they have to plan out what is going to happen in Idiot Abroad and he probably thinks up some comments beforehand, but it's still mostly his thoughts.
Have you read any of his books?
It's funny reading the words because you can just imagine him saying it. The ending of the first series where he goes to Wales pretty much all came out of the book he wrote years before, about how his holidays were always to Wales and they were probably the best he ever had.
As far as Idiot 2 goes... I'm enjoying it, but probably wouldn't say it's been quite as laugh out loud funny as some of the stuff in the first series so far.