Not without significant support from the outside and a lot of importing of materials and food. I mean, you could probably find some reason for some group to "start a new life" there. But keeping it maintained is a completely different story. That would require a lot of foreign investment, and a significant reason for said foreign investment.
The problem is that Antarctica's easily-obtainable resources can probably be obtained elsewhere with less trouble. Whales, coal, and petroleum can be found plentifully in warmer, less ice-ridden areas of the world. Now, in modern times, there have been a lot more resources found in the interior...but exploiting them has been banned until 2048.