You'd probably need the Fuegians to develop a more maritime culture, and then island hop around Tierra del Fuego, South Georgia/South Sandwich Islands, and eventually to the Antarctic Peninsula. The Falklands might also be settled in this case.
Still, it's pretty marginal, even for this culture. I'd expect the numbers to remain extremely small, no more than a few thousand. The Inuit are a good example for how this culture will function, but there's some key differences. Plants will make up a smaller part of their diet than the Inuit. I don't believe there are many species of edible plants in Antarctica, although they do exist. Key nutrients and fat can be gained the same way the Inuit get them--use every little part of the animal, and eat lots of blubber and fat.
In any case, they'll probably end up extinct within a century or two because of the breakdown in their society that sealers and whalers will cause. They live in prime sealing/whaling waters, and they will be visited often. Since they will be so reliant on the sea, and will However, their existence might lead to claims (probably British) over Antarctica and possibly also lead to further British interest in Tierra del Fuego, which will have major repercussions in politics in the Southern Cone. It also makes me wonder if the British might try and settle Inuit there at a later date to try and enforce their claim through colonisation, but I suppose if the Antarcticans are still alive in reasonable numbers, they'll suffice. Another key development is that this will almost certainly mean there will be no Antarctic Treaty. Various nations will try and claim Antarctica, even though the Peninsula will be securely British (unless Britain loses an ATL Great War and their Antarctic claim is given to Argentina or Chile or something). Mining operations may occur in Antarctica as well, and the continents resources will be much more known than OTL. This could mean that come the 21st century, it has a few thousand people, an economy akin to Svalbard (with more tourism), and has its own local government. I don't know if they'd mine the rest of the continent. They might, which might give you some more Svalbard-esque economies around the coast, but on the other hand, people might eventually realise that all that mining might not be so good, as well as issues in profitability, so the Antarctic Peninsula might just be grandfathered in on a continent-wide mining/exploitation ban. On the other hand, tourists will visit Antarctica far more, and I'd also expect the population of researchers to increase as well.
Could make for an interesting TL centered around Antarctica and the Southern Cone, even if the Antarcticans themselves will be a supporting role, even if an extremely important one at that.