The PS4 software details are now confirmed, its running a derivative of FreeBSD. OpenJDK already runs on FreeBSD x64, so should already be working (or at least pretty close to doing so).
So to make it usable probably just needs some sort of binding to the PS4 audio and graphics libraries. So good news on that front.
Also interestingly the PS4 has full WebKit support (including WebGL), the PS4 UI is even done using WebGL (so likely an OpenGL driver in there somewhere).
So technically doesn't seem like any big hurdles to get Java on PS4 (no sure about the legal hurdles e.g. licences, restrictions by Sony, etc).
We just need someone with access to a PS4 dev kit and the inclination to get their game working with Java.
I'm a Java developer, and we're working on acquiring a dev-kit for our game. In order to not have to do an entire port to C++ or something, we're going to explore this avenue. My first guess was to try to start with OpenJDK as well. I will post here as I get more information.