If animals are pushed out of their habitats, will they die?

They die for the most part. And this does not relate to the survival of the fittest concept of evolution brought up by several respondents. Its simply a study in being thrown out of your home in a hostile (human and natural causes) world. Animals driven from grlands (and other habitats) take dangerous journeys to areas where competitors already have a stake; usually they start in suboptimal ("substandard") habitat. And even in those areas, competitors already have a stake (as do predators).