Update - Connected
I did find that I was able to connect my PS2 Slim to my Apple Airport Express via a Cat5e cable plugged into the LAN or Ethernet port on the back of the AirPort Express along with using the PlayStation 2 Online Start-Up Disc 4.0 Broadband Only.
I simply connected the cables turned on the system, selected Create New Network then Automatic/Cable DSL (or something of that variation) it saw the network, and 2-3 seconds later I was connected.
The entire process took about 2 minutes. *Note a PlayStation 2 Memory Card is required to save the network settings w/ about 1 MB of free space (little less).
In the visual below you will want to connect your ethernet cable to the port indicated which appears as <-> on the back of the AirPort Express.