The custom Processor will be created once for each request - https://github.com/ocpsoft/prettyfaces/blob/3.x/core/src/main/java/com/ocpsoft/pretty/faces/rewrite/processor/CustomClassProcessor.java
If you need to be able to do this kind of integration, particularly if you want a configuration element to live as long as your application, then I might ask what you are trying to do with it, because the PrettyFaces processor, while it can be used for this, is not very flexible, whereas...
OCPsoft Rewrite - URLRewriteFilter (the core for PrettyFaces 4) is capable of integrating CDI into your configuration, and gives you more power than you previously had with Processors from PrettyFaces, while still making things simpler... for example: you might want to use the CDI integration to scope your configuration, or inject database access classes.
https://github.com/ocpsoft/rewrite/tree/master/integration-cdi
You will have much more control using Rewrite, today (or PrettyFaces4 when it is released.)