Well, from BART CD, it should be possible (to extract files from Chest). I can't really imagine any other solution (because if you can't boot, you can hardly access the files on the disk).
However, it's rather unlikely that (any part of) BART CD went into the free version of avast! (because of the license fees to Microsoft); regarding the Professional version - don't know; it's probably doable (though some users might have problems with the size - the BART's installer is quite huge, and the program updates may be pretty big as well), but it's a marketing/sales decision, not mine