If yes, can we also get additional information about the network configuration?
One useful way to do this could be getting the SSID of the current network. Is there an API to do that?
Update: I found a similar question here:
Can the iPhone SDK obtain the Wi-Fi SSID currently connected to?
(Separate answer to preserve history etc.)
It looks like you might not be able to determine the SSID of the WLAN to which you're connected, at least in an app that will go into the App Store. These people use a private API - Preferences.framework - to get to the details of the WLAN (like "is it hidden?" "What's the name?" etc.).