You know what? I'll try to take the 'Possibly!' position on this one, as amazing as that might sound.
Okay, so my first thought was: you won't have enough people. I'd heard numbers like '10,000' as the minimum number of humans required to not run into genetic problems from imbreeding. Turns out that number may be too high. Recently, a scientist calculated that it could be achieved with less than 100 people. Which is doable since the population in Antarctica at any given point in time ranges from 1,000 to 4,000 individuals. I didn't see any numbers that would make that range impossible.
Next up: food. I mean, it's Antarctica. How are you going to feed people? But the more I dug in, the more this doesn't seem to be an impossibility. King George Island is on the 62 degree latitude line south of Argentina. It's far closer to the southern tip of Argentina than it is to the south pole.
The temperature range at King George Island might blow your mind. Did you know that US states like Minnesota have more severe winters than King George Island? That part of antarctica is not classified as having an 'ice cap' climate, but actually a 'tundra' one, and it actually currently has vegetation on parts of it. While that vegetation isn't edible, it's not difficult to imagine being able to adapt/protect areas to be able to grow crops. King George Island also has a large population of animal life as well (seals, penguins). And antarctic fishing is a thing - there are major fishing zones well south of the 60th latitude right nearby King George Island. Finally, King George Island is already the place a large percentage of the people on that continent are already located, so it's a natural spot to try to figure out what to do and how to survive.
So, all that said, it's time to go over some of the pretty significant advantages that the humanity side has:
An incredibly intelligent base population. It's mostly scientists there, after all. It's not like we took a random swath of people living in Podunk and threw them into the apocalypse. It's almost universally people who solve problems creatively for a living.
A large fishing network. The scientists probably aren't going to be the ones to first find the problem; it'd be fishing boats starting to return north. But this fishing network has on incredibly important facet: it's a communication network, and one that doesn't depend on people maintaining a communication hub. If you took a random collection of 4000 individuals, how likely is it that you'd have a hundred CB radios, a hundred VHF antenna/receivers, and a hundred family service radios? Thanks to the fishing fleet, you've got it. It's pretty much the only apocalyptic scenario I've heard of where communication is actually completely taken care of for you.
A deceptively wide range of exotic supplies. Think about it - where else in the world would you find an incredibly eclectic set of supplies than scientists doing experiments with who-knows-what in an extreme climate. How many seed samples do you think are down there at any given point in time? Bio cultures? Materials samples? Scientific tools? Chemical compounds? Etc.
An already existing large cache of supplies. They're already used to having to maintain large supplies "just in case". I'd expect that Antarctica is probably towards the very top of the list in terms of a "Days worth of supplies on hand" metric. They have to be. If our city runs out of water, we can ship some in from a neighboring area. If they run out of something, it has to be shipped from another continent.
A group of people already partially adapted to their environment. A lot of apocalyptic scenarios are people having to adapt to a completely foreign situation. Not this one - everyone there has already been adapted. It's not like we took people from Arizona and threw them into this - it's a group of people that were already down there anyway.