Highly unlikely. It would be written as a native C++ app. Whilst the .NET CLR is very powerful and highly performant these days, there just wouldn't be enough justification I don't think to design their web browser on it. Remember this thing will be targeting mobile devices too. So every little performance optimisation can save minutes of battery life which all adds up.

That said, I've always wondered what a JavaScript implementation built on top of the CLR might behave like.