In theory, yes.

In practice, this tends to be a difficult problem to solve because most Linux environments are managed imperatively/procedurally rather than declaratively, meaning that in order to revert to a previous state, you have to be able to run the exact commands required to do so. The traditional answer is to manage such a system with Puppet or Chef - thus allowing an administrator to tell the system what it should look like rather than how it should go about it - but that's generally yet another layer of logical overhead to be considered.

NixOS - in theory, at least - addresses this more fully by integrating declarative configuration rather pervasively throughout the operating system itself, rather than trying to just add a layer on top of the operating system in order to manage it. It relies heavily on the Nix package manager - instead of installing a program directly to the filesystem hierarchy, it installs it to an isolated folder named with a theoretically-unique hash, allowing multiple versions of the same program to coexist without conflicting (and allowing users to pick which version they want), making it painless to roll back software upgrades (just go back to a different selection of which package folders should be linked to, rather than having to manually remove and revert each package), etc.; NixOS leverages this package management system for everything, rather than just the software installed, and will create GRUB entries whenever you commit your configuration changes (by running `nixos-rebuild switch` or `nixos-rebuild boot`, causing an instant configuration switch or a configuration switch on next boot, respectively).

Other operating systems can hypothetically do this, too, and they'd end up looking similar to NixOS in terms of how things are organized and configured. As I said, I think that's probably the direction where most operating systems will eventually go.

So all the actual filesystem entries are basically soft or hardlinks to the most recently selected version?

Time Machine on OS X works that way (as do a few other incremental backup solutions, I believe). Notably in Time Machine's case, it hacks a way to hardlink to entire directories which haven't changed, which is normally not possible. (There's a parallel here with how immutable data structures are managed.)