Based on my current knowledge, I believe you are wrong. Firefox' Desktop Awesomebar (which actually predates Chrome's omnibox) does not send every keystroke to Google[0], and never has.
Even Firefox' Mobile Awesomebar doesn't do that[1] unless you click that "Yes" button.
On the other hand, Google's Chrome browser is clear about the fact that it does send everything in the omnibar[2]:
> When you type URLs or queries in the Chrome address bar (omnibox) or App Launcher search box, the letters you type may be sent to your default search engine so that the search engine’s prediction feature can automatically recommend terms or URLs you may be looking for.
If you still believe you are right, I would be interested in seeing your sources.
Huh. Your first link says nothing about search suggestions. I based my comment on my experience of having to disable search suggestions every time I start a new browser. I hope you're right…
Obviously, I can't prove that it doesn't send search suggestions by giving you a link to the code, since it isn't there. If you want to make sure for yourself, I advise using Wireshark.
Oh. The search suggestions I get come from my DuckDuckGo Plus extension (installed it a long time ago). But my point stands with other browsers: Opera, Safari, and IE all have the unified bar, and I was referring to those browsers in my comment (specifically Safari).
References:
"Get predictions in the address bar" https://support.google.com/chrome/answer/95656?hl=en
"Logging policies for omnibox predictions" https://support.google.com/chrome/answer/180655?hl=en