Unfortunately, it won’t. Because the old Plex server version that you are using won’t get patched in any way, except by way of releasing of a new Plex server version – which won’t run on your old Windows version.
With proper preparation and calm step-by-step action, you can do it too.
See for example Attempting to move Plex Media Server settings and database to new windows server - database error - #3 by OttoKerner
Don’t forget to export your Registry data, for a truly seamless migration. https://support.plex.tv/articles/201539237-backing-up-plex-media-server-data/
