You can't do this with the default AIR installer. You would have to write your own installer or have the installed AIR app locate and copy the assets on first run.
I'll pursue having my AIR app copy the files from the CD on first run.
Joe, do you happen to have experience using other installers with AIR apps? Any recommendations/suggestions/warnings to offer?
No, I don't have any recommendations. You would need to sign up for the AIR redistribution program. When you do this you gain access to some tools that help the process. http://www.adobe.com/products/air/runtime_distribution1.html
The only warning is that you will have to create an installer for each of your target platforms (unless you find an installer product that is also cross-platform, of course).
Thanks again for your time, Joe,
I'm already signed up for the runtime distribution program, so that's covered. I'll look back through the runtime distribution docs again.