Yes, they do. I guess it depends on what sites the forum recognizes (blindly embedding everything it sees doesn't seem to be a very good idea I think). The forums work just fine with YouTube and Twitter links. No asciinema for you however.
I don't think the mods can answer this question, which might be why it was ignored the last time you asked that. I don't think I can answer it either but I tried.
Please take this comment with a tiny grain of salt, it is written at 10PM and it's based on about 10 minutes of looking around the forum software's website and its own forums
