I've seen all manner of responses to Google's announcement of their Chrome OS... but again, I have to stress that from what technical info that's been given Chrome isn't going to be a real OS, just a bare minimum "sandbox" for the Chrome browser to run inside. If Anandtech got their info right then the only thing this OS can do is run Chrome, no other programs or extras are allowed.
If it can't be run inside the browser then it won't be run... which makes a bit of sense given that most of Google's apps, everything from Gmail to Office to Google Chat already run inside the browser, even the search box doubles as a complex calculator. Therefore, the only data Google would be privy to is the exact same data they would be privy to as if the user was running Chrome as their desktop browser and already using these apps.
Of course the info I'm basing this on could be wrong, but supposedly they got it directly from Google and I've yet to see anyone showing evidence otherwise.