Your AirPods Pro here are a device you connect (pair) to your iPhone. In various ways, they’re a fancy wireless version of wired headphones many of us have and still use. The short-range connection used is known as Bluetooth.
You’re going to be learning a little more about the iPhone, as the AirPods Pro aren’t really at the core of all this. The iPhone is.
You can download music to your iPhone prior to the flight, and can then play that music to your AirPods Pro while in flight, without needing a network connection, yes. This while the flight crew allows use of electronic devices.
There are various ways to download and keep music locally on the iPhone, depending on how you store your music and whether you subscribe to certain services.
If you subscribe to Apple Music, you can add music to your library and into playlists, and can then mark specific playlists to always be kept local to the iPhone, for instance.
You won’t be able to stream music from Apple Music or any other streaming services while in flight, though. Not without a network connection, and that usually means paying for the connection. If one is even offered.