You can do it if you put it in a template (ETA: but that's not the same as posting it, so that probably doesn't help). I think you can also do it if the forum allows html, but I think that's something you don't want to do in general. Maybe you could allow HTML in a forum only moderators can post to, if that works for you.
BTW, just to save you time - you can't enable HTML, post something, then disable it, it won't work
What are you using for youtube? Maybe it can be modified.