Yes - the mechanism varies based on the submission that's used. If you use JMF submission then you can also setup a persistent subscription to the MIS system to get status on all jobs submitted to FFCore via JMF. If you use JMF you can alternatively include NodeInfo information in the JDF to enable status signals on a per job basis. If you can alternatively include ReturnJMF information which will enable a single ReturnQueueEntry signal when the job completes.
If you are using MAX or HF submission then most people that do this will use a script and the external workflow component to send a signal to the MIS system. The external component will perform a CLI call that you can use to invoke a script for updating status on the MIS.
FFCore can also add a barcode to the job to facilitate post-print job tracking.