Was the system booted to Windows? I think this is the reason at least Kaspersky Rescue CD uses some kind of Linux bootup.

The Avira AntiVir Rescue System bootable disk is Linux-based. Here's an excerpt:

The Avira AntiVir Rescue System a linux-based application that allows accessing computers that cannot be booted anymore. Thus it is possible to repair a damaged system, to rescue data or to scan the system for virus infections. Just double-click on the rescue system package to burn it to a CD/DVD. You can then use this CD/DVD to boot your computer. The Avira AntiVir Rescue System is updated several times a day so that the most recent security updates are always available.

Also, there are directions on installing to a bootable USB stick here using UNetbootin. This article also confirms that you can update the antivirus definitions via the Internet.

A bit offtopic about malware. When will the world be freed from the broken shit called Adobe Flashplayer?

http://www.theguardian.com/technology/2015/jul/08/warning-adobe-flash-vulnerability-hacking-team-leak

I've lost count how many times there is a quick hotfix for Adobe due to vulnerability where your PC can be taken over. No wonder porn sites seem to love Flash player, as it gives them means to inject malware to visitor's PCs.

More to come, I'm sure.

According to the article (at bottom) for installing Avira AntiVir Rescue System to a bootable USB stick:

Note
You do not have to download a new .iso file every time. If you have an Internet connection, you can easily update Avira Rescue System.

Assuming the virus doesn't cripple your networking capabilities, I would think that would answer your question in the affirmative.

Most likely the virus will itself want to connect to the net in some way, so I quite doubt it'll flash the network card's firmware with something unusable, and anything beyond that won't affect a rescue boot disc.