No, you can just run the systemd init system and not use any other systemd programs.
I would probably run systemd-journald just because it's really nice to have a logging system which knows about the system services, but it's not required.
You probably also want to run udev, and logind comes close. Everything other than these four is absolutely optional.
You probably also want to run udev, and logind comes close. Everything other than these four is absolutely optional.