A good question and one that requires a great deal of thought.
I don't think that Antarctica's development is inevitable, but it is possible. I don't think that it is rapidly approaching either - though it depends on your definition of "rapidly".
As long as the rest of the world is stable there is no need to populate Antarctica, it is just too expensive to do so and at the moment any settlements - scientific bases - are totally provisioned from outside Antarctica.
It would need some momentus change in the world to populate Antarctica with a sustainable economy of its own with any degree of self-sufficiency.
The most extreme glabal warming forcasts however do predict this momentus change, with changes in sea-level due to rising temperatures and raised temperatures in the tropics making many places in the world uninhabiatable or even just not there any more - and they'd be under water. In this scenario, Antarctica could become somewhere to live and could probably support a large population of people in some degree of self-sufficiency.
There is a historical precendence in that part of Greenland from about 1000 A.D. to approx. 1400 A.D. had up to 5000 viking people living there until the climate became too cold for their continuation see here
. Also, Antarctica has been forested in the past while in pretty much its present position, so if the ice melted, it could become so again.
I do tend to feel however, that we (mankind) has a love of fantastic stories beyond reality, and while we should maybe give more importance to global warming and its effects than we are at the moment, that we should spend more time on what we know to be true and less on what sounds extreme and more exciting.
Also, see this page on Cool Antractica about global warming in Antarctica