Its pot luck. The trainers did not work on the DLCs when I used it. But for others it did.
I have most of the DLC if not all dloaded and it worked great. One of the best games I played this year.
[Edited by element5, 2/22/2014 4:30:55 PM]
Current version still working (PATCH 08.26.2013). I just tried it.