It is very difficult to say as it depends on the distance from where the medical emergency happens to Port Stanley, Falkland Islands, or Ushuaia, Argentina. There are no helicopter nor plane evacuation possibility from South Georgia and the South Sandwich Islands, nor any medical facility that will be able to help with a serious medical situation in this area.
It will take at least 2-3 days from South Georgia to Port Stanley and similar if a medical emergency happens between South Georgia and the Antarctic Peninsula. All scenarios are highly weather dependent.
In the Antarctic Peninsula we have a chance to use the air field at Frei/Bellingshausen station at King George Island, South Shetland Islands, but this is not a given thing and needs to be arranged in advance. Assuming that such arrangements can be made, evacuation time may be between 1 - 2 days depending on weather conditions. If flight arrangements have been possible to arrange but the weather does not allow the plane to land or the evacuation from ship to shore (only possible via Zodiac), it could delay a medevac or consequently force the ship to Ushuaia in order to complete an evacuation.
We are far away from any possible medical facility in this area and any evacuation scenario takes a lot of time and could have a devastating effect on the rest of the trip for fellow travelers.
Therefore if you are in poor health or in doubt, please consult your physician for a check-up that you are healthy enough to travel to such remote places with limited to no medical facilities.
On our motor vessels we have a qualified physician onboard on all trips. The infirmary onboard our motor vessels is merely suited for first aid medical care.