As I was about to call it a night, I noticed that Leopard had automatically created an icon for "oracle's remote desktop" in the Finder. Double-clicking on it yielded nothing, so I almost just gave up and went to bed. I figured that I'd check the console of my Windows box just in case it was asking for something.
Turns out that the icon is a link to start a VNC session with the Linux VM running on that Windows box. Tweaking the VNC server settings just a spot to allow access without a prompt was all I needed to do. Next time I double-clicked on it, a new window containing the desktop of my Oracle Enterprise Linux VM appeared:
Sure, you can go and configure all of this manually, but it's nice to see this type of "techie" tool seamlessly bundled into a product that is also aimed at complete tech novices.