So does it actually accomplish any privacy protection? There are two cases:
You blindly type in your search query into the Awesomebar and it works correctly. For users that do this, it works just like Chrome, no privacy protection.
You use the provided search bar for searches, and Awesomebar for URL's. Your searches are in no way protected. This does protect the URL's you type in, such that example.com is not sent to Google/Bing/Yahoo/DDG/etc. as you type out "example". Did Mozilla actually show that this is worth protecting, and that most people don't just type in "example", hit Enter, go to Google, then click on the first link? This is what I see 99.9% of users doing already.
Note that the autocomplete can pick up the difference between a URL and a search by the presence of a pattern that doesn't follow a URL. Chrome does this. Type in "example.com" vs "?example.com". The "?" is specifically there to indicate that you want search. Perhaps privacy conscious FF users could learn this shortcut, and everyone else can get the convenience they expect?
I am not trying to downplay the importance of privacy in browser implementations, just questioning the privacy implications of this feature.