Os 9
As of now, yes. Downloading and converting to an .mov or similarly old file is the only way. Sebastian Patting (lowendmac.com writer) managed to hack flash 7 with good ol resedit to look like flash 9 and that worked for a little while. It screwed up the player window in classilla, but youtube moved on and it no longer works. There was another trick circulating (making it look like embedded video) but for me that no longer works either. Someone was working on a Mactubes like application for OS 9 called macflv, but I think he is a student and not devoting much if any time to it these days.
For youtube lack of any H.264 support in OS 9 would be a major hurdle to overcome, and one Cameron Kaiser is understandably not all that interested in working on. He's talked about some HTML 5 support, but likely that would not extend to video. Kaiser says Classilla 9.3 will be focused on the mobile web, ie pushing users towards mobile sites, which load much faster without all the modern java script and ajax.
I will try to install a simpler script in Classilla, I was pretty amazed it installed at all frankly.