There are actually two different kinds of A-GPS as best I understand it.
One is the bad kind where GPS only works when you have a cell signal. It offloads a lot of the processing to the cell tower. This is used by cheap phones to comply with FCC requirements for location reporting for 911 calls, and isn't found much elsewhere.
The other is the good kind where it grabs the almanac off the network when possible for faster cold start times. This kind still works fine when you have no connection, it just takes longer to figure out your location when you turn it on, because it has to download the almanac the slow way.
They're basically unrelated except for the name, which is confusing.