No, Metro stuff can be written in C++/C#/etc - it's just a different set of APIs to target. As I understand it, Chrome/Firefox would have to be ported to run on the new Windows Runtime. I have no idea how difficult that would be.
I have had a quick look at it, in order to port different applications.
It is doable for complex application, but is a lot of work, especially for rendering and GPU acceleration.
If your application relies on MFC, Webforms etc, then yes... it would be a lot of work to port it over to Metro UI but this is not the case for web-browsers where 99% code is already cross-platform and completely independent of GUI.
So for web-browser, this is not a matter of "porting". It's a matter of adding new "chrome" for WinRT.
