If I back-up my virtual servers, and then there’s a catastrophe and I need to build a new server and restore my backups to the new server, will the passwords still work if I do not store passwords in plain text?
If they are system passwords AND the version is still supported, then yes.
I did a move that has some very old password hashes and the version of Debian I moved to didn’t support the old format. I was able to configure support for the old format however. This is an unlikely occurrence but it does happen.
Now if you have programs that store their own passwords then that is on them.