Firebase should definitely work.
- You will primarily be interacting with it via the REST API
- You will need to ensure that the correct permissions are present in manifest.webapp. Especially the systemXHR permission
I have written a tutorial on writing a Firefox OS App that is powered by another mBaaS : Kinvey. Conceptually things are similar and you could take a look : http://rominirani.com/2013/08/19/firefox-os-tutorial-episode-10-using-mbaas/