The browser could pick a fake screen size, and behave in a way that is consistent with that fake screen size. This would probably break many sites, but it would mitigate fingerprinting if a common size was used.
I doubt that is avoidable, as the browser would still probably need to render at the false viewport dimensions. For a common adversary, fingerprinting based on timing would be more involved and less useful.
Firefox had better make sure its timing is not affected by such shenanigans, for instance.