I’m confident that Mozilla Corporation doesn’t want to support an officially branded Firefox for Android that doesn’t have the full complement of Web Platform features. (In this case, GCM is required for Web Push, which is a big part of the Progressive Web Apps strategy on mobile.)
So while it’s technically possible, it’s not something that Mozilla is likely to commit resources to. I am interested in doing small things to ensure that downstream projects (including, but not limited to, F-Droid) can build a free-as-in-freedom Firefox for Android without fragile build system hacks for the foreseeable future.
That means that F-Droid will need to continue branding Firefox for Android, just like it does now.