In airplane mode, everything is turned off, even GPS, read the support page here:
http://support.apple.com/kb/HT1355
Also, AGPS is not wifi triangulation. AGPS is assisted GPS which uses cell towers to speed the time it takes to get a GPS fix.
If what you want is to save battery and not use data, turn off Wifi and Bluetooth on the first page of settings, then go to General, cellular and turn off cellular data