Seems like a pretty obvious "no" to me. Loudoun County is a much better choice, just to pick one alternative. Antarctica is an awfully inhospitable place and running a data center there would be a nightmare.
And yet it's way better than space. It's much easier to get to. Cooling is about a thousand times easier. The radiation environment is much more forgiving.
This whole concept is baffling to me.
(Incidentally, a similar thought experiment is useful when talking about colonizing Mars. Think about colonizing the south pole. Mars is a harsher environment in just about every way, so take the difficulties of colonizing the south pole and multiply them.)