You should have GPS without any service at all. You might need data for the map to load, depends on the app. If you’re lucky and the app automatically cached it when you had signal, or you manually downloaded the offline map, then you could navigate home in airplane mode.

All of this is moot because I think I remember reading the rest of this story. The hiker wasn’t really lost, they simply went on a hike without telling anyone, and ignored calls during that time because they were trying to unplug.