They mention in the talk that the satellite will periodically downlink both its location as well as where it thinks the particular spot beam you're using hits the earth.

So while at the very least I'm not sure you'd get GPS-quality data, if you monitored that data for awhile I'd think you could eventually get "good enough" accuracy.

I've also read about the Syrian bombs targeting Iridium users. Maybe they used triangulation to locate the source of the signal that was being broadcast from earth. Does/did the Syrian govt have that tech? Would they need satellites, or would helicopters be enough? And which government/supplier did they buy it from?

I remember hearing that as well, although I can't find a citation.