In Darwin this is not a theoretical question. A storm takes the mobile network out for an afternoon, a flight south is four hours, and the answer to "does this game work offline?" turns out to be four separate answers depending on which part of the game you mean.
What usually keeps working
The board itself. Once a level pack is downloaded, the puzzle logic runs on your phone and does not need anything from a server. You can open the game, select a stage you have already reached, and play it exactly as normal.
What usually stops
- Life timers. Many games verify the clock against a server precisely so people cannot skip waits by changing the phone's time. Offline, some freeze the timer; a few refuse to grant lives at all.
- Events and leaderboards. Always server-side. Progress made offline sometimes syncs later and sometimes simply does not count.
- Advertisement rewards. There is no advertisement to watch, so the free-booster option disappears.
- New level packs. The most common failure: you play to the end of what has been downloaded and the next chapter will not open.
- Purchases. Obviously, and worth knowing before a long flight.
The preparation that actually helps
Open the game on wifi the day before and play a few stages beyond where you are. That triggers the download of the next pack. Then check the settings for a "download all content" or "reduce data" option — some games expose one, and it is the difference between four hours of play and twenty minutes.
Second: make sure you have signed in with whatever account the game supports. Progress made offline on an anonymous local save is the progress most likely to be lost when the app finally reconnects and the server disagrees.
Screenshots from the official Australian store listings. All rights remain with the publishers.
Which of the four here holds up best
The plainest games do best, which is not a coincidence. A title with no events, no leaderboard and no daily wheel has less to lose when the network goes, and a title built around a city that unlocks with timers has the most. In our testing during a couple of storm outages, the two simplest games on this site kept playing normally and the building-based one became a menu.
A caution about aeroplane mode as a strategy
Some people put the phone in aeroplane mode to avoid advertisements. It works in some games and, in others, produces a permanent "reconnecting" screen or quietly loses the session's progress. It also removes the free-booster path, which for a player who does not spend money is a bad trade. Worth knowing before it costs you a chapter.