Well, it turns out to be possible and indeed rather simple, so this hint is almost obvious when one thinks about it later. So, let's begin. I'll assume that your AirDisk is set up with accounts to access it.
- In your Mac OS X 10.3.x Panther Mac, open a Finder window and click on the Network icon in the sidebar.
- Choose your AirPort base station and connect to it by clicking on the button.
- In the dialog that appears, connect as your AirDisk account (the same as your local user account), choose to remember the password in the Keychain (in order to automate further accesses), and select all available volumes.
- The AirDisk volumes will now appear in the Finder: mine, for example, are called AirDisk (the main, shared volume) and Sven (the user account volume).
- Open System Preferences and click on the Accounts preference pane.
- Drag the AirPort Disk volumes to the Login Items (I think it's called so in English, but whatever the name is...) section of the Accounts preferences and optionally choose to hide the items.
- Log out and in again: the AirDisk volumes will now mount automatically! (And if you receive a Keychain reminder during this setup, choose to always allow the access, in order to automate the process as much as possible.)
[robg adds: I can't confirm either the problem or the solution, having no access to a 10.3.x Mac.]

