In theory, sure, but only abstract theory. In reality there is always an eventual limit on available resources of water, land, food, etc. So unlimited growth over time will eventually exhaust the resources. This is nature's way of preventing overpopulation beyond that which is temporary. Another way to put it is that nature always corrects itself eventually, and this is one way.
In terms of ecological communities, they can only continue to increase as long as there are resources available to support the growth. People, plant life or animals cannot survive without adequate shelter, food sources, clean water and sufficient protection from disease. The extent to which these resources are available and adequate protections exist will determine how long and how large an ecological community will exist. All of these factors can be thrown into chaos, however, when faced with natural disasters, i.e. the Earthquake in Haiti, the Tsunami in Southeast Asia and West Africa, Genocide, civil war, etc. Those forces can destroy entire communities and cause them to have to rebuild from scratch. Therefore, the growth is not linear and may actually decrease significantly until stability is reestablished and growth can continue to occur.
I had to add one thing to this set of answers. There is indeed a set definition for the term "community" in ecology--it means the interactions of a group of populations of organisms (plants and animals) in a set area. As it is in a defined area, there is generally a limit to how big it can grow as a whole. But also, since the resources are limited and the organisms compete for them, the number of the various types of organisms are related to each other. If, for example, something happens to the birds that eat a type of insect in the ecosystem, the number of those insects will increase temporarily. The increased number of those insects mean that whatever THEY eat will show a decrease--and then the insect population will go down, as they don't have enough to eat.
The second poster is correct. No ecological system can support unlimited expansion of a population, even when that system is fueled by the seemingly limitless energy of the sun. When it comes to modern humans, too, population size isn't the only concern; the population's patterns of consumption could grow unchecked and cause serious harm to the ecological system even if the population of humans were to remain stable.
If you are interested in exploring this topic further, I recommend that you read about "the Club of Rome" and "sustainable growth" and "limits to growth." Be aware, of course, that people have strongly held opinions when they feel threatened in their lifestyle, e.g. that someone might take away their Hummer or force them to recycle. You are likely to find very strongly worded criticism of the ideas of "sustainable growth" and, especially, "limits to growth," but these are very real concepts that we are likely to have to grapple with for years.
Ecologically speaking, no community (I assume you mean a population of some kind of organism in a given place) can increase indefinitely.
This is true because of the ecological idea of carrying capacity. This is the idea that any given environment has a finite amount of the resources that a given organism will need. If the population of that organism expands too much, it will exhaust those resources and the population will fall.
This phenomenon can happen with animals or with human beings. One example of this is how deer in the eastern US sometimes outgrown their resources because they lack predators. In these cases, many of them starve.
Honestly, in a fantasy world, this may actually happen. However, in the real world, a population is able to increase only until the carrying capacity is reached. What this means is that once food, space, and other resources run out, the population will not be able to increase. This would mean that there would be competition for survival and Darwin's Theory of Evolution by Natural Selection. Only the 'fittest' organisms would survive and reproduce. The others would eventually die or move, due to lack of resources.
The first thing that one has to consider when looking at an ecosystem is the available resources that can sustain life. If the resources get used up then life ceases to exist. For example, a study was done using rats. The scientists set up a habitat for the rats that included enough food to feed ten rats comfortably. There was actually a bit of overabundance in the food supply so the rats gained extra weight and were quite well. The rats began to multiply. (The food nor available living space was not increased). For the first generation born, the food was adequate. The next set of rats born led to weight loss among the control group and some fighting over food and space. By the time the population had increased to fifty rats, the rats started killing each other off for food and fighting all the time. They were self-destructive and in the end of the experiment had reduced the population by extreme measures including eating one another's young. Only one member of the original control group had survived. I do not recall the group that performed the experiment, but I learned about it in sociology in college. It had made a big impression on me.
The experiment demonstrates that a community can not expand indefinitely because resources necessary for survival will decrease and the life forms will begin to diminish. Some theorists believe that war is one of mankind's indirect means for population decrease in order to sustain resources for other groups.
The question is somewhat vague.
Ecology is a branch of science that deals with study of relationship that exists between living beings and of all the living beings with their environment. There is a branch of ecology called human ecology that deals with ecological aspects of urban environment. It is not clear if the question relates to ecology in general or human ecology in particular. Depending on that a community may mean community of any living things in any setting or just urban communities.
In any case the term community is not a clearly defined concept in ecology. For example when we consider the impact of pollution of a river, we are interested in only the community living along the river. However when we talk of greenhouse gas effect and global warming, the entire world becomes a single community.
In human ecology we may define as an urban settlement with no discontinuities of non-urban areas as a single community. In this sense we can stretch our imagination to visualise the world as one continuous urban conglomerate with no non-urban settlements at all. However this can only be a theoretical imagination rather than a reality.
So we can say that in theory ecology does not explicitly rule out the possibility of a community that continues to increase indefinitely. However, it is a situation that cannot exist in reality.