As long as that content remains on the same console then yes. DLC, of any kind, will only work offline on the original console it was downloaded to.
I read something somewhere once that each console's ID number is attached to the DLC so if you move it to another console, for whatever reason, you'll need to be online, with the same account you used to download it, for it to work. A prudent security measure, but a bit annoying on those days when the server crashes.