I think I see what you are trying to say, but I don't think the Boltzmann Cake Theory is comparable to Many Worlds.

In the Boltzmann Cake case, it may be impossible to physically test the theory (though I don't conclusively assume so -- there could well be some very subtle effect on the Sun's output that would facilitate such a test), but the question of fact it raises is still of objective fact.

But the truth or falsity of the Many Worlds Theory can only exist in a reference frame which spans the entire conceptual space in which the many worlds would have to coexist. And I don't believe such a frame can exist. The very fabric of logic itself requires a space-time in which to exist; without one (or extending beyond one) its very postulates become open to doubt.