I'm sure his writers will remain American.
Oliver does perfectly fine without being American. In fact it gives him a better perspective for broader global issues. I'd imagine Trevor will have some interesting things to say about immigration, for instance.
Oliver immigrated here and worked for a long time on the show. But even Oliver didn't completely replace Jon like what Mr. Noah is doing.
Plus if they think the show is going do have the same ratings with more international reports they have another thing coming. So much of the backbone of the show has been reports of odd or eccentric America stories or poignant observation of hypocrisy or the American political system. Only 36% of Americans even have passports and it would be safe to assume that many of those have not left the nation.
If Noah intends to do more international flavored reports about say Greek austerity, Germany and its influence in the EU, England media or its instance of very public compulsory surveillance and its movement towards internet censorship its not going to get the same reaction from the American audience.
I think part of the reason why the show worked that despite uncovering the flaws of America you could tell that there was still a deep ingrained love of it. Like having a child that wets his bed over and over again. Sure you are pissed that you have a mess to clean up and it and it almost never seems like its stops but that doesn't stop you from loving the kid.