Sure you can.
Here's an example how:
<div id="content">
# Welcome
Hello. Welcome to my **website**.
</div>
<script src="https://cdnjs.cloudflare.com/ajax/libs/showdown/1.4.0/showdown.min.js"></script>
<script>
var conv = new showdown.Converter();
var txt = document.getElementById('content').innerHTML;
console.log(txt);
document.getElementById('content').innerHTML = conv.makeHtml(txt);
</script>