How to see the filenames imported by the Feeds module?
Imported files are stored in default/files/feeds by default I think so you could test on that first.

Feeds does create a watchdog event but it doesn't persist.

If you attach feeds to a node then you have several advantages. You can re run the import. And more interestingly you can access the node via Views and probably Rules. With those two you could build something with a Rules trigger event on the node save or Feeds import that would check for an existing node with a matching file.

If you can't get that working then post back and I'll try to make an example.