No, no it absolutely would not. It would continue being more or less the same for animals. Right now, in regions mostly uninhabited by people, animals perpetuate the "circle of life", which includes prolific rape, brutal violence, infanticide, cannibalism, and breathtaking amounts of murder, for reasons ranging from desperation to sport.

It's not any different with people here. Sure, the habitat would change, but with changing habitats come changing species anyway. The last ice age allowed for the development of gigantic mammals who could roam far and wide in search of food. The end of that ice age saw a similar destruction of habitat. Cities are a new habitat that is ideal for some animals: rodents, decay-eating insects, small animals of all kinds. And if cities were to lose their human population and be grown over, that would be ideal for a different subset of species. Hell, even if the world fell to nuclear radiation, the roaches would still have a home.

There is no 'garden of eden'. The idea that there's a 'perfect earth' is an illusion. The earth just is how it is, same with all the people and animals alive on it. The earth doesn't discriminate against viruses, invasive species, or the most successful of them. Algae caused the first great extinction, still algae survives. The earth doesn't have any special love for the gentle, kind, or beautiful creatures. They exist and like everything else, function in balance with it.

Human beings included.