just my $0.02 anyway..
I think by definition that divergence is instant. But then that brings up another can of ethical (or more exactly, lack thereof) worms.
Anyone agreeing to this would have to do it KNOWING that they were committing genocide. On themselves and humanity. And when the last human replicated and eventually died, humanity would cease to be. And all the moral constraints that governed that humanity along with it.
There is simply no need for morality when one can simply be replicated or disposed of/scrapped/erased.