How many people are going to live there? Supported by what infrastructure? How is the infrastructure going to be maintained? Where are all the machines that you need to repair and replace the infrastructure? Where are the plants to produce the machines? Who is going to maintain the infrastructure, the machines and the plants? How do you decide who's going to get to Antarctica? How are you going to prevent other from going there themselves? How are you going to stop the rest of the world from nuking Antartica in retaliation? How are you going to stop the USA and China from going to war over that last habitable piece of earth? How are you going to provide food and oxygen to the few survivors?
Not really.