You would still need a server to host your Plex. Usenet is just the source of your files. You would use a downloader like SABnzbd to download and unpack your files. You can then point Plex to those files if you wanna access them on your Plex.

The only thing that changes when you switch from torrent to usenet is how the files are downloaded. The same way you can torrent at home, you can also download from usenet at home. It's just that if you have a server, you can offload all the downloading and unpacking to the server, and you can also use Plex to share it with your friends, etc.