Nope, AGPS isn’t required. At any given time, multiple cell towers can hear your devices signal. In the rare event it’s just one, you still get a surprisingly accurate location due to a quirk of cell towers (there’s never just one antenna, except for small cells in places like subways, it’s usually three or more using sector panels). Given a 120° direction (or less) and a distance based on time of flight, you usually get within a few blocks in most cities, and that’s without factoring in triangulation or other more advanced localization techniques. One carrier (maybe more) has the ability to localize a person with a range of ten feet (not everywhere, but enough places to turn it into a product they sell), which is generally more accurate than AGPS.