Assume no. Recreational drones are generally not permitted on standard IAATO coastal Antarctica voyages, and recreational use is prohibited in South Georgia without an authorisation most travellers will not qualify for. Drones are subject to strict rules in Antarctica and they are not a normal passenger packing item. If you want to bring one, you need written approval from your operator plus confirmation of every regulation that applies to your itinerary, and you should sort that out long before you pack rather than at the gangway.
The reasoning is the same one behind the wildlife distance rules. A drone is a disturbance to animals that cannot tell it from a predator, and the industry's whole licence to operate rests on not doing that.
Don't assume that because one operator permitted a drone on one voyage, yours will. Satellite communicators, heating appliances and high-capacity batteries sit in the same category of things that vary and need checking rather than assuming.
Ask us and we'll get the position for your specific departure in writing.