My Precise machine was previously working fine, but now when I update from update-manager or the terminal I get an error about being unable to authenticate google-chrome.
There seems to be one file missing from the Google download server -- see http://crbug.com/249188.
Until that's fixed it would be OK, but not entirely safe, to update without checking the signature.
If someone can intercept and interfere with your internet traffic they could send you a malicious replacement for Chrome, so I wouldn't do this over public wifi, for example.
update: Now it's fixed.