The short answer is no. Evolutionary theory does not "prescribe" that a species should survive. Additionally, evolutionary theory expects that there will be a certain percentage of any population that will refuse to procreate, whether it be by an abnormal behavior, like homosexuality or an unwillingness to mate, or by a behavior that is advantageous to the gene pool, such as mating rights. And even a member of a species that does not procreate can still increase the chances of some of it's genes being passed on to the next generation, for example by caring for kin, which increases the probability that the genes shared by related individuals will be passed on to the next generation. Though ultimately, I'm not sure how relevant the example you present is to evolution, since the fact that a species will go extinct if none of its members procreate is true regardless of whether or not evolutionary theory is correct.