I believe that is true only for the "time to first fix" at a new location (a long ways from the last place you used it). As I understand it, any GPS needs "almanac" and "ephemaris" data to function. This is the data that tells the GPS where to look for satellites and enables the GPS to calculate your location from those satellites. Which satellites are available depends where you are on the surface of the world. The satelillites constantly broadcast this data, but it is slow to download. Your stand alone GPS stores the data for your current area. If you turn off your GPS, then travel a few hundred miles and turn it back on, it takes some time to download the new data, and this slows the first fix. With AGPS your cell phone first tries to grab that data off the cell network, and that speeds up that first fix.

Putting your iPhone into Airplane mode also turns off the GPS. In normal mode your iPhone GPS will still work fine without access to a cell network. However your mapping functions will not work without the network, unless you have downloaded and stored the maps on the phone. The ability to do that depends on the app.


EDIT - Regarding iPhones, GPS, and airplane mode, see the Apple Support Pages note iOS: Understanding airplane mode: