My impression is that it's unnecessary for a conforming browser.  (Note that the browser cache doesn't matter; we don't serve app.manifest with the caching headers turned on because we want the browser to fetch the latest version from the server whenever the browser checks; but on the other hand if the manifest file itself ends up in the application cache the browser won't update to a new version regardless of what the caching headers are set to).

It's easy to test for a particular browser: take the line out and see if the client still updates with new code.

However, leaving it in doesn't do any harm; while this is speculation, if perhaps some browser version somewhere might get confused by the "/" fallback entry and leaving it in would prevent the problem, we would avoid a nasty bug.