I don't know for sure, but I heavily doubt it, as it would open up so many potential security holes.

The standard way to access files for extensions seems to be with Native Messaging: https://developer.mozilla.org/en-US/Add-ons/WebExtensions/Na...

Basically make the user install a small program on their PC, then your extension talks to that program, the program reads out the file that you need and then hands it back to your extension.