A video has been posted that shows that you need to be logged in to Xbox Live all the time to play Plants vs Zombies: Garden Warfare.
For some reason, none of the game modes in Plants vs Zombies: Gardem Warfare are playable if you are offline. You need to be online to play any of the game modes. Even “Garden Ops” and “Options” cannot be accessed unless you are online enabled.
There is an offline 4 player co-op mode for the Xbox One version so maybe that version of the game is playable without the internet.
Check out the video below of Plants vs Zombies: Garden Warfare requiring you to be online: