I guess fall detection only works if you have a data plan or are carrying your phone (if you don't have a data plan) ?
As an example, last week, I was out doing a running workout with my S7 watch (it has no data plan). I don't carry my iPhone when out running as my watch still tracks my route so no need to carry the phone also.
During the run, I stumbled over a short small tree stump, which sent me flying to the ground hands out first, however, the momentum from the fall sent me into a sideways roll and I managed to roll through it and then got back up and carried on running.
There were no notifications from the watch about a possible fall - perhaps because my movement carried on after the fall (not sure?!)....
🤔