I finally managed to get ADE 4.5.1 to work under PlayOnLinux. I'd rather be running 2.0.1 but at least I can read my purchases. Appropriate comments in stores, complaining about inability to read because of OS unsupported by Adobe, have been left.
Reading through Adobe's forums, it seems ADE is a problem child on every OS. And Adobe is TERRIBLE with support of this program. I wonder why they don't publish an API for the content network. Then they wouldn't have to worry about maintaining client software and could focus on the servers.