Are there any PokeStops or Gyms in Antarctica?

Yes, there are Pokéstops/Gyms/Ingress Portals in Antarctica. There is only one legitimate way to get access to these locations short of being Tony Stark. You have to be a part of the United States Antarctic Program, and then actually go and live at McMurdo station.

Internet access and WiFi is available, however access to it is tightly controlled due to limited bandwidth. They are limited to a 20Mbit/s satellite connection to Sydney which is shared across the base.

Back in early 2015, a few Resistance agents were actually down in McMurdo and took it upon themselves to clean up dodgy portals that had been submitted by GPS spoofers. The saga they went through to do so is worth reading in its entirety here but for those of you that want the TL;DR, they had to get permission to have a laptop connected to the McMurdo LAN, create a WiFi hotspot off the laptop, then use line of sight WiFi repeaters to actually get data access at the locations. They submitted several portal move requests, an invalid portal report and submitted several new portal requests.

So yes, there are several locations in Antarctica, mostly around McMurdo station, and going there simply to play Pokémon GO isn't a realistic* option.

_{* I suggest that if you are going to do so, you send Niantic a little FYI email with proof of your trip in triplicate and get a written response from one of their community managers because I can guarantee that your account will be reported by numerous people.}