If you have Classic installed (OS 9.2) on the PowerbookG4, yes it should run.
If you have a folder called "System Folder" (not System, that is OSX) or if you have a System Preference called Classic, you have Classic installed.
You may or may not have an installer CD for classic included with your original Powerbook CDs.
Sounds like you got your monies worth out the laptop and 2.1 TIME TO UPGRADE
You would not believe all the new features. Come out from under the Rock.