Good point, I hadn't thought of the auto complete. I figured you were more referring to the actual query itself which Chrome already sends home to Google via it

Good point, I hadn't thought of the auto complete. I figured you were more referring to the actual query itself which Chrome already sends home to Google via it's cloud synced web history. In which case it does not matter whether you use the omnibar or visit the website directly as long as you have history sync enabled.