Question: I've downloaded the IOS5 IPSW from Apple's site and want to update it from within iTunes. So, 

* Does the update require an Internet connection?
* Does the iPhone switch off/reboot just as the update is initiated?

I ask because I'm at my new place where I'm yet to setup an Internet connection & my iPhone tethered to my laptop is my only Internet connection. I don't want my phone to be bricked because it cannot verify the update or what-not because there's no Internet connection.

Answer: 
Yes it does. It has to verify the firmware with Apple's servers (gs.apple.com). If it cannot, it will error out (usually presenting a 3XXX error, which is quite often 3004) and fail to update.
it does require internet. Just made the answer short.