While using a non-primary console, you must have an active Internet connection to play downloadable content.
If you lose your Internet connection while playing downloadable content on a non-primary console, your game will pause after a certain amount of time; however, once you connect online again, you will be able to resume from the point you left off.
More:
https://en-americas-support.nintendo.com/app/answers/detail/a_id/22448