This story of aGPS so far seems fairly reasonable and straightforward, but alas it is not. See aGPS is not some monolithic, written-in-stone-standard. In fact, Qualcomm, who makes the most popular aGPS chips (called GPSOne) has four different possible configurations for aGPS. How aGPS is actually implemented on the device appears to be up to the device OEM/cellular carriers.
These four options are:
* Standalone - Your handset has no connection to the network, and uses only the GPS satellite signals it can currently receive to try and establish a location.
* MS Based - Your handset is connected to the network, and uses the GPS signals + a location signal from the network.
* MS Assisted - Your handset is connected to the network, uses GPS signals + a location signal then relays its 'fix' to the server, which then uses the signal strength from your phone to the network towers to further plot your position. You can still maintain voice communication in this scenario, but not 'Internet/Network service' ie Web Browser, IM, streaming TV etc..
* MS Assisted/Hybrid - Same as above, but network functionality remains. Normally only in areas with exceptional coverage.
btw, I have a phone that currently has aGPS in it that operates in stand alone mode so I don't know what your definition of a real GPS is but, I can get GPS sat coordinates in airplane mode on my phone.