Yes, Narrative works fully offline for both culling and editing. Once you've installed the software and logged in at least once, you can use all core features without an internet connection.
If you want to receive the latest updates, you will need to connect back to wifi.
Getting Started Offline:
Install Narrative and log in while connected to the internet
Once logged in, you can disconnect and use Narrative offline
Open Narrative anytime - no internet connection required
Reconnect to wifi to receive software updates and feature improvements
Tip: If you're traveling or working on location without internet, make sure you've logged into Narrative at least once before going offline. After that, you're good to go!