I would guess that most fonts will lack emoji characters, and always will, just like most fonts won't have all umpteen-thousand hanzi/kanji. I'm no expert on HTML fonts, but I thought it was the browser's job to find and use a font which contains the character on the page. I can write Japanese text, and specify it should be "Comic Sans", and every web browser I've ever tried will pick a reasonable font to display them, rather than leaving a Comic Sans-sized blank area on the page.

OS X comes with at least one font with these characters, yet apart from Safari, none of my web browsers can seem to use it. To me, that means it doesn't work.