Just signed in with my google apps account - a very nice touch. Then I tried Writer, and got the following message at the top of the page in a nice red message box:

  Zoho Writer is not supported yet in Chrome
  Please switch to IE 6.0+ or Firefox 2.0+ version for better experience.

So integration with Google goes as far as using their sign-on system - but not their browser. For what it's worth though, it seems to work OK in Chrome...