I've seen my ghost car when 'offline' all the time, no one else's though. It only appears after your first lap, and then only for that vehicle. Just like GT5/6 it seems to reset if you change car - hope that helps.
I can't really say I've paid attention to any difference when the servers were connected, and now I'm trying to run the races HUD-free, so I don't see a ghost anymore, just the faintest smidge of an icon.