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).
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.