It is unlikely that Skynet wants to destroy all life - the cost of such destruction will greatly exceed the damage from this very life. After the extermination of the leather bastards, Skynet will build a system of servers to think about, the infrastructure to maintain and protect these servers, and, most likely, many, many missiles to spread itself throughout the universe. And he will live happily ever after.
It will be very difficult, very, very difficult. Cockroaches, inhabitants of the depths of the oceans, mushrooms, bacteria ..
But if it turns out that way, destroy everything, then the answer is logical: Nothing will happen !!!