WinRT will have the same popularity as Windows phones (translation: no one will care about it.) Thus, I absolutely don't care what browser they will put on it.
Windows was only popular because of their previous success, or I should probably say, because competition was asleep at the wheel .... now they latch on to a larger market share only because of the corporate world that is slow to respond. (Many are still running Windows XP family software.) Things will go downhill pretty rapidly for Microsoft when they release Windows 8 and abandon Windows XP, let alone Windows 7 and a familiar Windows architecture -- i.e. Start button, control panel, x86 and x64 apps.