It is possible, but it appears that it involves editing multiple Firefox files. Please check out this thread from more details.

I did see this post but I wasn't sure how it applied to the current version of Firefox. browser.jar no longer exists. I did find that omni.ja replaced browser.jar

When I extract omni.ja there are multiple browser.js files that all seem to be located within dev or test directories.

Has anyone disabled file browsing in recent builds of Firefox?

You could also try downloading the Public Fox extension to disable the file://C:/ domain.