Pega's File Listener rule doesn't support connecting to the FileNet system as a Listener. But I have seen a few customer implementations using IBM FileNet as a CMIS provider. That's to facilitate storing Pega attachments/files externally. Not applies for your scenario posted.
If you can get the new document pushed into Filenet be made available or copied to a place/directory which is accessible to Pega. Then you may configure File Listener to process the file every time it's pushed(created) and create a case based on the information read.