If you install linux on the PS3, it can ofcourse run Java. But my sources indicate that it has little resources, and the requirements for installing are a little tough for the regular gamer.
The JVM installed on PS3 is placed there to meet the BluRay standard to show menus and stuff, called BD-J. From what I can gather after a quick Google, its an interpreted JVM, which is far slower than a regular Sun JVM. The PS3 is claimed to be one of the fastest, but probably not optimized in any way to cater for the multitude of Cell processors. And the BD-J does not help running Java applications in the web browser.
So, why would we want a native JVM on the PS3 specialized for Cell? Because it's damn cool :) Perhaps for running web servers. But a JVM capable of running Applets in the PS3 Web Browser could mean that Sony could capitalize on the enourmous amounts of Java games located on the web available freely to PS3 owners. Ofcourse, the native games will still have better funding and perform better, but allowing free applications could create the same community of developers and games as Apple has benefited from. Without the drawback of locking in developers to a single platform.
Apparently, running games off a USB memory stick works. Will be back with more on the subject