Given how things are going, possibly yes. If a perfect storm forms in the shape of lack of food, lack of water, lack of usable land, wars, revolutions or conflicts, then the toll could be extremely heavy.
Let's hope it doesn't become like Calhoun's rats:
" Using a variety of strains of rats and mice, he once more provided his populations with food, bedding, and shelter. With no predators and with exposure to disease kept at a minimum, Calhoun described his experimental universes as "rat utopia," "mouse paradise." With all their visible needs met, the animals bred rapidly. The only restriction Calhoun imposed on his population was of space--and as the population grew, this became increasingly problematic. As the pens heaved with animals, one of his assistants described rodent "utopia" as having become "hell."
Males became aggressive, some moving in groups, attacking females and the young. Mating behaviors were disrupted. Some males became exclusively homosexual. Others became pansexual and hypersexual, attempting to mount any rat they encountered. Mothers neglected their infants, first failing to construct proper nests, and then carelessly abandoning and even attacking their pups. In certain sections of the pens, infant mortality rose as high as 96%, the dead cannibalized by adults. Subordinate animals withdrew psychologically, surviving in a physical sense but at an immense psychological cost. They were the majority in the late phases of growth, existing as a vacant, huddled mass in the centre of the pens (with their mobile phones,Twitter accounts and virtual reality goggles
). Unable to breed, the population plummeted and did not recover. The crowded rodents had lost the ability to co-exist harmoniously, even after the population numbers once again fell to low levels. At a certain density, they had ceased to act like rats and mice, and the change was permanent. "