I don't see why it would need to be affected.
The constraint to require a valid signing isn't something imposed by the license on the Android code. If you want to distribute a version of Android that doesn't check for a registered signature, that should work fine.
I mean, the Graphene guys could impose that constraint. But they don't have to do so.
I think that there's a larger issue of practicality, though. Stuff like F-Droid works in part because you don't need to install an alternative firmware on your phone --- it's not hard to install an alternate app store with the stock firmware. If suddenly using a package from a developer that isn't registered with Google requires installing an alternate firmware, that's going to severely limit the potential userbase for that package.
Even if you can handle installing the alternate firmware, a lot of developers probably just aren't going to bother trying to develop software without being registered.
That's actually a really interesting question.
I understand that Apple takes issue with packages that can themselves "take packages". But historically, I don't believe that Google has. Of course, Google also hasn't done the registration thing historically, either.