Is A-GPS also working without an active 3G contract?
Say I buy an iPad 3G with an operator SIM card in place but don't pay for 3G service, will A-GPS still work or not?
The GPS will still function, but it will take a bit longer to lock onto your location. Also, note that the built-in maps app doesn't have maps stored on the device. It downloads them real-time. This will work fine if you have WiFi, but not if you're offline.
To use the GPS for offline navigation, you'll need an app that stores the maps locally.
Here are some options:
NAVIGON Mobile Navigator has pretty good reviews. It's $59.99 in the US Store, and it also works with the iPhone.
CoPilot Live HD is half the price, but the reviews for it are pretty bad.
More info from Apple: (Click for source)
So, in essence, it works with our without a cellular connection or WiFi. It's just faster with it.
One more source: A thread on this very question in Apple's support forums.