It gives JavaScript access to its very own, empty, sand-boxed VFS. However, you can give the page access to directories manually with drag-n-drop or a directory selecting input tag. So if the app needs access to just one parent directory then you're good to go. If you need the app to have indiscriminate access to the entire filesystem then you might be able to give it C:/ (or whatever other root dir) but I have never actually tried it.
Given Google’s shift to focussing on standard and standards track web platform features in Chrome, and tendency to eliminate everything else, I wouldn't bet on this (which predates that strong focus) being around forever.