If I have a phone with airplane mode turned on, can it turn itself off automatically (without user interaction)?
Airplane mode will stay on as long as you don't set it to turn off on its own.
A forced system update, for example, will apparently disable airplane mode.
This can happen without user interaction.
However, such automatic deactivation of Airplane Mode for a system update would generally require the user activating WiFi (after entering Airplane Mode) or some other communication channel that allows the phone to become aware of the requirement for an update.
Also, some apps can activate and deactivate Airplane Mode, if permission is granted. This is especially true for older (<4.2) versions of Android.