Not on mobile, which is where Facebook wants a browser.
I think people are not seeing the forest from the trees here. Firefox has a lot of potential on mobile phones, because Firefox has a lot of desktop users that would want the Firefox on their mobile devices, at least for the Sync functionality.
Also, on mobile WebKit may be the most popular, but there are so many incompatibilities and performance differences between Android's browser, Blackberry's browser, the webkit-powered S60 browser, Chrome, Safari and Mobile Safari that you might as well count those as different engines.
[1] http://www.gsmarena.com/1ghz_s40based_nokia_c3015_pictures_s...