tl;dr: Yes, but probably takes some effort for most content.

Plex will play the files, but metadata is hit or miss. If it's something that's on thetvdb or themoviedb, it can be matched as a series or movie, respectively. With some effort, you could also probably include all the relevant metadata when downloading the videos, then have plex use local metadata, which could cover anything not big enough for the big metadata providers.

I think it's also possible to find plug-ins/scripts that will pull metadata directly from youtube, but I've had bad luck relying on that stuff and then development stopping, so I avoid it these days.