Short answer is: I think this is in the wrong area.
Long answer: No. The BART (bootable anti-virus and recovery tools) disk is not a normal operating system, as it's a variation of the windows PE format.
IE it runs off of a CDROM.
As far as the Avast A/V product goes, I do not believe it does contain a firewall.
Please do a search in the forum and there are lots of notes and reviews on firewalls and their intergration with Avast.
Cheers
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W0mbat