If this device supports Java, I think Processing can run on it.

No, but if you offer me such device, I sure will find out...

Seriously, I don't know what you mean by "set up Processing". You probably be able to run applets there, if the Java plug-in is installed in the browser. Perhaps you can run exported applications if you have a script launching Java with the exported jars. If you want to run the PDE, it can be a bit harder, but unzipping a Linux archive, seeing how it is run (perhaps via a shell file) and trying to run the appropriate jar to launch it might work.
Note: what can fail are features using native libraries, like Movie, Serial, Minim, etc.

Well, as I wrote, all you need to run an applet is the jar, and a way to run Java by passing the name of the jars in the command line. And you are still restricted on libraries with native libraries (including OpenGL, unless JOGL has been ported to the Blackberry hardware).
OF has different problems. IIRC, it is a C++ framework, so they need to compile the libraries and the program themselves for the device's CPU and system. It is a harder problem. If Java is already running on the device, the hard part have been already done. One advantage of Java (old motto is: "write once, run everywhere", at least everywhere you have a JRE...).