Cellular E911 uses handset GPS on most CDMA networks (which can not be disabled by the user) and on some GSM networks location is determined pretty quickly by differential time of arrival at a couple of nearby sites. If no GPS or TDOA info is available the PSAP gets cell tower location and bearing derived from the site and sector serving you.

Your location info is supposed to appear immediately at the turret position that gets your call, in CDMA the 911 operator can "re-bid" the phone manually to force it to resend location info while your connected to them.

I have heard instances where the 911 operator was relaying GPS coordinates to a SAR helo in decimal degrees (41.002343/-73.213456 for example) and the crew was inputting the location as Degrees-minutes-seconds (41 deg 32 min 45 sec/-73 deg 31 min 22 sec). Unless its up on a map display and you have everyone on the same page for coordinates this is another potential point of failure.