Yeah, I noticed Google Chrome recognized it automatically. I just didn't see it at first because the fragment identifier wasn't updated when I searched.
I've been pondering about that too (mostly something with having a service worker drawing each char on a canvas, uploading that to a server), but keeping track of OS/Browser/vendor/font-setup/... (let alone getting it all out of the browser) makes it pretty hairy to get right.
I think something simple would add alot of value and separate you from other similar services :). Wouldn't be wrong with icons from os/browsers but just he 2 biggest would add value too.
For example if I see the icon from the most common IOS-version looks bad I won't be using that particular charcode.
EDIT: It does: http://charcod.es/#%s works fine