OK in the sense of being uncomfortable overpopulation can happen. Japanese subways are like being packed in a sardine tin can. But its population hasn't made it impossible to feed people. People are not dying because the population is too big. In fact Japan's birth rate has fallen below replacement levels and they are worried about it becoming more difficult to pay for a future aging population when there aren't enough working age taxpayers.
Japan proves this point particularly because the country itself doesn't have a lot of natural resources. And yet even with a large population density, largest density in the world in fact they're fine.
Japan suggests that if the population gets too dense it starts regulating itself.
Another densely populated country India is not even a developed country yet and its birth rate is declining as the population gets more dense.
In 2012, Japan was only 39 percent self-sufficient on a calorific intake basis when it comes to food production. Furthermore, imports account for almost all of their primary resource requirements. People are not dying and their standard of living is high only because it is artificially propped up by cheap energy and Japan's economic ability to import goods. If oil were become $500.00 per barrel, Japan and similar countries would be cast back into third world status.