Is it ever safe to restart the repository box but not the core?
The core is continually using the repository (even if jobs aren't running). So if you were to turn off your storage unit that the core uses for a repository, you would first want to shut down the core service itself, as it is a safe bet the background tasks are running without you knowing. Once the core service itself is stopped, then reboot your storage.
Don't have to reboot the core server itself, but you'll want to stop the service and then start it once the storage is back online.