shouldn't be, it's just a browser that gets you onto the internet, not part of your computer as such. Is your scanner still not working when you're not on the internet?
Your browser should have no influence on the way your scanner works. Rather than trying to fiddle with settings delete the scanner in your devices and reinstall with the latest driver from the manufacturers website. This wont take very long.
As has been said, there's no connection between any broswer and scanning software (although I can't think why you'd want a browser open when scanning something anyway).
CAC's suggestions of uninstalling the scanner driver, and then reinstalling it, looks sound to me. (I always like to restart a PC in between uninstalling software and then reinstalling, as it flushes the registry so that the new installation can't pick up on anything left behind by the old one).