I've noticed this feature when using the incognito mode. It's almost like the experimental feature from Chrome OS: Google's mobile interface no longer includes a search box and the query is displayed in the omnibox, where you can change it. If you go to google.com, you'll still see the regular Google search box and the query won't be displayed in the omnibox.
The query is preserved when you switch to other search services like Google Image Search, Google Video. Unfortunately, there's a bug that replaces the query with the Google search URL when you pick an image search result and go back to the list of results.
I still think that integrating Chrome with Google Search so tightly is a bad idea. Removing an essential navigation feature from a web page and moving it to the browser makes Google more difficult to use (users will think there's something wrong, other browsers show a different interface) and a small Chrome bug can prevent users from editing a query.
Another side-effect of the integration is that Google will not show search suggestions in the incognito mode. It's a regular feature of the omnibox that will make Google more difficult to use. All of this for shaving a few pixels and showing more content.