Not really, natural immunity exists in both groups (vaccinated and unvaccinated) because they vaccinate people with natural acquired immunity too. Maybe the younger ones (< 50) have more natural acquired immunity because some of the older ones have not survived the process of getting immune. They have tried many times to show us that people with natural acquired immunity need vaccination to become fully protected. But they could never show that in real live. What they can show is that the number of antibodies gets even higher after vaccination, but it seems that it makes no difference if you can kill the virus or if you can double-kill it.