I wouldn’t put it that way. They don’t share the “library sharing” information, but the sharee information is shared (so-to-speak) 
i.e. you won’t need to re-invite your shared users, they will all be still there. But you need to edit each one of them, to add permission to access the libraries on your new server.
A different approach would be to “clone” the old server, like so: https://support.plex.tv/articles/201370363-move-an-install-to-another-system/
This will transfer both the access permissions of all shared users and their “played” status over to the new machine.
However, without additional measures you cannot switch on the old server again afterwards: I want to backup my Genre tags from one server and restore them onto a new server - #3 by OttoKerner
