From my understanding it doesn't rely on the internet or Garmin servers. I believe it was called Iridium satellite network. It needs to work anywhere on the planet. It is a separate subscription based service.
So if Garmin's system is down, there is a very real risk that these services won't have anyone on the other end to answer the call.
Update: The use GEOS https://www.google.com/search?client=firefox-b-1-d&q=garmin+...
edit: Thanks!