Is it possible restore or update your iphone if you only have tethered internet? I totally bricked my iphone for a couple of days last time I tried to upgrade my OS.

I didn't realize that upgrading the OS requires access to Apple during the installation process. I only have wireless Internet that is tethered from my iPhone.

So last time I tried to upgrade, I downloaded the OS, then proceeded to run the installation, which  shuts down my iPhone in order to install files. After that though, it requires some sort of verification from apple.com and because my iPhone is already shut down, i have no Internet access.

I ended up having to go to a friend's house to the install cos she has WiFi.

So is it possible to upgrade with tethered internet? Is there an option where you can do the verification before re-installing. It just seems strange cause although it may be rare to only have wireless internet, I'm sure I'm not the only person to have ever encountered this, and there was never a warning message that it couldn't be done before the installation.
As you said, yes, you do need to have a connection to download and verify the install, not just the download. Its the computer doing the update that needs an internet connection - not really the phone. 

In your case, the phone is currently in the update, which is probably running a very 'light' iOS bootstrap while your computer does the update. OS features like tethering would not be running then (nor anything much really), and so your computer would not recognize it as a connection, and the iPhone can't really do the verification in its state at that point either. 

The only way you could really do the update with tethered internet is to have another iPhone that you are tethered to.