Correct me if I'm wrong, but I gathered from the blogs n such that once c3 is loaded then an Internet connection is no longer needed at all to be able to use it. If that's true, then once c3 is loaded you should be able to disconnect from the Internet and keep using it no problem. The only thing that wouldn't work is saving to or loading from Dropbox or the other online file hosting services.
Actually, I'm curious to try something now. What if you closed the chrome browser with c3, disconnected from the Internet and re-opened the browser and tried to load the c3 website? I seem to recall Ashley talking about offline cache in his blogs... I'll have to try that tomorrow.