Just tried that (Firefox 25 on OSX). It didn't work. Down arrow does nothing, and there are no AwesomeBar matches, so there is no drop-down. Maybe you have some configuration option set?
Nope. When you type anything in the omnibox that chrome thinks is a url, it shows atleast 2 items in the dropdown one is go to url and other a search google for url. I can upload a screenshot when I am back home in a couple of hours.