It's possible in theory, but in practice it would be hard to get it to the point where it works the same as it does in javascript and html5. Not to mention it would be hard to update it to stay on par with c2 releases.
Now if you utilized a javascript engine like v8 or spidermonkey you can get most of the way there with most of c2's runtime running as is you just need to impliment html5 stuff like images,canvases, input, etc in c++ or something.
I was able to do that with a couple hundred lines of Python with v8 and sfml as the input/graphics backend. It just runs an html5 export to do it. I've been meaning to covert it over to c++ to eliminate the overhead of Python. But anyway the idea is to just impliment the system specific stuff in c++ and run everything else with js.