Godfall will require an always-on internet connection regardless of what mode you're playing.
Confirmation first came via the game's PS5 store page, which stated: "online play [was] required". Confused, some gamers reached out to the developer via Godfall's official Twitter account for clarification.
While the response was keen to assert that Godfall should not be categorised as a "service game", it "does require an internet connection to play" (thanks, VG24/7).