The idea is that you write apps in HTML/js/etc, using some well-defined APIs to access the underlying hardware capabilities.
The implementation is an underlying Linux system (Gonk), and Firefox's rendering/javascript/etc engines.
If you ask, 'can it run alternate browsers', what exactly are you asking? The browser app of FF OS is written the same way other apps are -- in that sense you definitely can. But it'll still be running on top of Gecko et al.
Ok, so can you replace Gonk/Gecko with some other underlying implementation? Well, that's kind of the whole idea! But if you do that, you won't be running FF OS anymore.
The reason we care about alternate browsers is choice. FF OS enables choice by promoting standards. They want an app written for the system to work just as well on Chrome or Safari (whenever Google/Apple get around to implementing the same APIs.)