While it’s theoretically possible, I’m not sure it’s actually going to work well.
You can move the server data directory to another drive – though this can significantly impact your server’s performance.
You’ll also need to re-link all those special configurations to point your future Plex Media Server to the same external drive/share (Registry configuration). Overall it might be easier to look into some decent backup approach or simply copy the old server’s data directory to the new device.
https://support.plex.tv/articles/201370363-move-an-install-to-another-system/