That seems to be the case with me too, since I do not see the “script blocker” splash screen on Firefox startup, but it shows up on IE7. However, in the Customize/Protected programs portion of the Script Blocking provider portion of avast!, it shows “Mozilla” as one of the programs that can be protected. What is that, if not Firefox?
Personally I would leave it on as technically there is no overhead if you aren’t using it, but it would be there in the unlikely event you did use IE, like for windows updates, sites that don’t display well in firefox, etc.
The browser extracts the scripts from the page and passes them to Script Blocker. It scans them for viruses and if everything is OK, the browser continues execution. There’s no whitelist… and the scanning itself shouldn’t affect the execution in any way.