If you create two SPANs, one containing the character you want, and the other containing an unprintable character U+FFFD (�) is a good one, then you can test whether they have the same width.
<div style="visibility:hidden">
<span id="char-to-check">♯</span>
<span id="not-renderable">�</span>
</div>
<script>
alert(document.getElementById('char-to-check').offsetWidth ===
document.getElementById('not-renderable').offsetWidth
? 'not supported' : 'supported');
</script>
You should make sure that the DIV is not styled using a fixed font.