In theory, yes. In actuality, that will never occur, as someone would have noticed the problem by then, and taken steps to control or relocate the population, if possible.

By then the world would've resorted to China's one- or two-child policy

I think by then the world's population would have corrected itself..through disease, starvation..any of the factors that cause a population to drop...

A good thing us humans dont get along and kill each other. IN BIG MASSES.

We actually reached that point a long time ago. Earth can naturally sustain about a billion of us. That means without tractors, irrigation pesticides, herbicides, hybrid plants, genetically engineered plants, yada, yada, yada. We could raise enough food on the naturally arable land area to feed about 1 billion. To use reasonable amounts of those artificial systems without draining rivers poisoning the land, turning to hybrids and genetically modified plants and animals, earth can sustain 3 billion. In order to sustain the 6.6 billion (and growing) we need to turn to severe methods to irrigate - like draining whole lakes and rivers (Chad Lake is gone, as one example). We need to use chemicals which leech into lake and river and have reached the oceans killing large areas of sea life. We need to over fish the seas - over 90% of the ocean life is gone - we are literally scrapping the bottom f the barrel when it comes to fishing. There is not enough clean fresh water to go around. We have tapped all the ground water (wells) and sadly many places have to cap their wells due to pollutants. Areas that still have clean water are finding the water table going lower and lower with each passing year. Our technology is what sustains us. Without it most of us would starve or die from disease. We have surpassed the reasonable limits of this one planet 30-40 years ago. By 2050 the population will reach 9 billion. By that time places like the USA, UK - were talking rich nations, will be no stranger to famine, thirst, and early deaths from diseases due to the weaknesses of starvation and of course from the amounts of pollution. By 2070 we will have empties the oceans of fish we can eat. By 2050 most of the corals will be dead. IF we continue down the road we are going, in less than 100 years the biosphere will fail, and humanity will most likely be either wiped out or brought very close to extinction - not so much through famine and disease, but by the wars that will be waging for the dwindling, limited resources. So no, humanity will never reach population to where our species will every spot of ground. We will however reach a number which will lead to a major die off. It happens too all species that over populate their ecology.

Some people think that even if this could eventually be the case, it would not be a problem because we would have the technology to colonize other planets: 1) "A cornucopian is someone who believes that continued progress and provision of material items for mankind can be met by advances in technology. Fundamentally there is enough matter and energy on the Earth to provide plenty for the estimated peak population of about 9 billion in 2050. However, this must also mean that there is enough for the current world population but starvation and fuel poverty have not been eradicated, suggesting that the problem is not a lack of resources but the distribution of said resources by the current economic and political system. Looking further into the future the abundance of matter and energy in space would appear to give humanity almost unlimited room for growth." Source and further information: http://en.wikipedia.org/wiki/Cornucopian 2) "Overpopulation refers to when an organism's numbers exceed the carrying capacity of its habitat. In common parlance, the term usually refers to the relationship between the human population and its environment, the earth.[1] Overpopulation is not simply a function of the size or density of the population. Overpopulation can be determined using the ratio of population to available sustainable resources. If a given environment has a population of ten, but there is food or drinking water enough for only nine, then that environment is overpopulated; if the population is 100 individuals but there is enough food, shelter, and water for 200 for the indefinite future, then it is not. Overpopulation can result from an increase in births, a decline in mortality rates due to medical advances, from an increase in immigration, a decrease in emigration, or from an unsustainable biome and depletion of resources." Source and further information: http://en.wikipedia.org/wiki/Overpopulation

Millions of people die every year from starvation, dehydration, disease caused by inadequate living conditions and general neglect. This is below most people's radar though as it occurs mostly in third world countries. Space is not the issue, resources are.