If it does, don't they cease being black holes? (If the smearing is larger than the Schwarzchild radius - obviously, that requires really small black holes...)

Which seems to be really useful if you want your point particles not becoming black holes upon creation. If you think about it, every classical electron should be a black hole, it is already thanks to quantum physics that this is not the case.

I'm not an expert in quantum gravity, but as there's no widely accepted theory of quantum gravity I suspect the answer is: we don't know.