The Custodian would let you set up a distribution for the job log files so you don't end up having thousands in one folder. This would let you keep the job logs separate from the application if that's what you need.
But another approach would be to use Datawatch to read its own job logs on a periodic basis - say daily. A DataPump process with one project that opens *.xml in the job logs folder, and a model that checks the XML content for whether the job was successful, and and OLEdb export to a SQL database of your choice. An input distribution can then store the source XML files in an archive.
If you would like a sample model, do feel free to drop me an email.