Possibly, but there would be very little need for it or use.
As far as we're aware there are very few resources in the Antarctic.
Furthermore, living conditions are harsh and extreme.
A severe lack of sunlight for long periods of the year make it difficult to farm, alongside the fact that much of the continent is ice and rock with little to no soil.
As a result any farming would have to be hydroponics, which can be expensive to build a large enough amount to provide constant nutrition to a large population.
There's also very little in terms of nutritition available in the form of animals.
Rearing livestock would be difficult as very few farmable animals are capable of surviving the environment, and to bring them to the Antarctic would require their own food-sources to be available. Another challenge in providing via farming.
We could use fishing, yet this is left to the coastal regions of Antarctica.
This would mean that very little of the landmass of the continent is used.
A further problem with living on the shore however is the fact that the continent is subject to very rapid and extreme shifts in weather every 6 months, as the continent experiences Summer and Winter.
In the Winter large areas of the sea will freeze over, preventing fishing.
In the Summer large areas of land will thaw away, cracking the land. This would damage any structures around and prevent large permanent residences.
Water is also difficult to acquire. There aren't many (if any) rivers on the continent, and any water is either found in the sea or is trapped as ice inland.
Sea water is salty, and therefore requires both pumping and filtration to use.
Ice is similarly difficult to use, as it requires carving out of the ground and thawing. (I don't know what the composition of Antarctic Ice is like, so it may too require filtration).
We would also be damaging ecologically, as our presence would ultimately affect those species of animals that do currently live in the Antarctic, such as Emperor Penguins, birds of prey and Seals (particularly Elephant Seals, who would definitely be hunted for their large meat and fat reserves, which provide good food and oil for burning).
Add in a larger presence of polluting machines which would definitely be used, both for transport and generation of heat/electricity/water, and we would be directly polluting into an area of the world which there is already concern over, in regards to the effects of Global Warming and pollution upon it.
I'm sure that we could colonise the Antarctic, but there would be very little need outside of scientific exploits.
If we were ever in need of space for living I think we would much more quickly head to planetary/lunar or even orbital colonisation first.
The Antarctic is difficult and harsh and provides very little.
There are also UN sanctions to prevent nations claiming the continent, so that would come into consideration too.