To save both client download time and network usage, is it possible to use the localStorage feature of HTML5 to store contents of linked stylesheets, javascript files and binary
I think in this case you should consider offline caching:
You can also store user input data in localStorage or sessionStorage:
Don't use globalStorage (not a standard).
I've written an article about offline, see: http://hacks.mozilla.org/2010/01/offline-web-applications/
It's about offline, but such mechanism can be used to boost your web app.
You could base64 encode your image/binary data and store it as a string in localStorage, using base64 urls doesn't work in a few browsers so it's not a perfect solution.
CSS and js would be fine, you could write them into the page, or use a base64 url also.
I wouldn't worry about doing this breaking the site for non JS users, as is JS is disabled you cant access localStorage anyway.