I just tested this with my Bluetooth unit and the latest version of the iPhone app.
With the phone in flight mode, the app tries to connect to the cooker "Looking for Anova…" It sits on that indefinitely, without any error or timeout.
With Bluetooth turned off, the same thing happens. The app waits indefinitely without any error to indicate that this cannot possibly work.
If both cellular data and wifi are turned off (but Bluetooth is on), the app correctly connects to the unit.
With both cellular data and wifi turned off, or with the phone in flight mode, tapping on "Recipes" brings up an error:
"Those darn wireless connections! We had trouble connecting, so make sure you have a strong signal and try again."
It would be better to display an error to say that wifi and/or cellular data need to be turned on.
With wifi connected, but no Internet connectivity ("Lie-fi"), the app says "Internal error". Room for improvement here, too.
But at least, with only Bluetooth working and no IP connectivity (data link layer or transport layer), it's possible to talk to the cooker.