Not really. Because the vegetation that grows back after a bushfire is more sparse: the bushes grow further apart and more of the top soil gets fried in the sun, killing the mycelium and other life that supports the growth of plants. This engineers an environment where only certain plants with specific characteristics can grow, in detriment of diversity.
The current rodent infestation in many places is due to unwarranted application of chemicals that kill the diversity that keeps the mice under control, like raptors and snakes.