I already tried it and it didn't work. I've had expired codes work on Xbox which is why I still went ahead and entered it.
I'm really disappointed by this too, as it not only has the extra playable DLC included, but also a dynamic theme which I was excited to use instead of that standard color background.
If the DLC is actually on the PSN as pay content you could always try calling Sony customer service and explaining it to them. They may have a way of issuing it to you without being charged.
If it is expired as in not even on the PSN anymore then there probably isn't much to do. You may even try contacting the publisher but I would try Sony first. You might get no where but it is worth a shot.
PSN ID: sled_dogs76 60" Pioneer Kuro Elite PRO151FD, Yamaha RX-V3900 A/V Receiver, Oppo DV983-H player. Coming soon: 2 Seaton Submersives from Mark Seaton