This used to be stated on the previous version of this website in the FAQ’s section:
Last Epoch will support both online-only and offline-only characters. Online-only characters will exist in server-authoritative multiplayer. Playing offline-only characters will not require an internet connection.
An internet connection will be required to update the game client, and you may need to activate the game a single time before play.
And this was from the March 26 dev stream:
Taking the two statements together, it would seem that something has changed since that original FAQ section statement. So I can only assume the vagueness in Mike’s answer is because they’re not yet certain how much online interaction the offline mode will require, or at least that’s how I understand it.