The browser has a local copy of the blocked sites database; so it doesn't have to do any extra request in order to check if a web site is blocked or not.
Google always cared about which website you visit. They are using javascript to dynamically change the destination address of search results on Google.com using an on-click... but I guess they figured that most people who uses chrome didn't bother to change the default search engine so the small percentage of bookmark browsing (that doesnt have Google services embedded) is not worth it.
Your premise about Google's motivation for creating Chrome is belied by the fact that they were dominant in search for years before Chrome came out. They never had anything to worry about there.
Being dominant doesn't mean that there is no foreseeable threat to dominance. Preventing a hostile browser monopoly which could work against Google's search dominance is a credible motivation for Chrome (though probably not the sole motivation -- moving web technology in a direction favorable to Google's non-search roadmap was clearly a factor, as well.)
Similarly, a major reason for Android could be seen to be preventing a hostile mobile-platform monopoly which would either block or extract monopoly rents from (and thus limit the value of) Google services reaching mobile users.
