Chrome on OS X 10.8 shows me a square, and so I assumed that the joke is that it represents Schr枚dinger's box -- you know, where he keeps the cat which may or may not be dead.
That being said, Emoji seem to work at least on Mac OS X (current) and Windows 8. Alas, Chrome doesn't render them within a page (but in the tab/title bar, maybe because the OS' rendering takes over there). Firefox and IE show them both, apparently (presumably because both are DirectWrite-based by now).
See http://apple.stackexchange.com/questions/41228/why-do-emoji-... for more details.
Also, I am not an expert about this so I could be wrong about the details.
Granted, this is on Linux, but I think it's only a matter of whether or not your font has glyphs for the emoji characters -- correct me if I'm wrong, but I don't see a technical reason to treat emoji differently from any other Unicode character.
Edit: changed glyph based on someone mentioning it had heart-shaped eyes
$ iconv --to-code UTF-32BE|xxd
馃樆
0000000: 0001 f63b 0000 000a ...;....