For up to 7 days.
Nintendo's FAQ page has revealed that Nintendo Switch Online NES games can be played offline for up to 7 days as long as you have an active Nintendo Switch Online membership.
It's not clear what will happen if the membership lapses during this 7 day offline period.
The short 7 day period isn't ideal for users like me who keeps their Switch in offline mode (powered off). If I don't go online before I go offline, my entire NES collection will be locked down if I wasn't online within the past 7 days.
Image credit: Nintendo.
- "Frequently Asked Questions (FAQ)." nintendo.com. Retrieved September 17, 2018.