Had flash not existed, I suspect they would have used another video playback plugin, or rolled their own. I don't think YouTube's success was dependent on Flash. But the ubiquity of Flash certainly didn't hurt.
Imagine YouTube depending on QuickTime, Windows Media Player, RealPlayer, or Java Applets. Flash's user experience was just so much better than those options. I'd guess that YouTube couldn't have had that much success were there not such a ubiquitous (and downright good) plugin.
