When you type into the chrome omnibox, it sends your keystrokes to Google to give you search suggestions. Just using those would be sufficient, and I don't think they really hide that it's sending your input along. If someone does a Google search for a URL, we expect it to get added to the index; why is it different when the search occurs in the omnibox rather than their web interface?
URLs don't go through google when you type them in Chrome's URL box, they go directly to the address. Chrome only sends things to Google that it can't interpret as a URL.
Actually it looks like URLs do go to google's suggestion service as you type into Chrome's URL box.
I tried typing "http://then and it suggested a UPS package URL and "thenicestplaceontheinter.net". I've not been to either of those pages before (I use Chrome for testing, so I'm not signed into it, etc).
