Stuff can break - there's not especially strong guarantees across versions, but if I, say, took /etc and /home from a Debian stretch system and put them on another Debian system, it would likely mostly Just Work.

It gets more exciting the further you drift - e.g. if you're going to Debian buster, or something more significantly different like Fedora/RH, you'd probably want to cherrypick config changes from /etc, though /home should be fine(tm).