Q: Sparsebundle won't mount

My wife's iMac (2007) had been backing up to an Airport Extreme (latest model) for a couple of years using an USB attached 1TB WD MyBook external drive. After reinstalling Mavericks 10.9.2 and moving her iPhoto library to Aperture she called in a panic and said most of her photos going back 12 years were missing. I confirmed that fact and attempted to recover them from the Time Machine backup on the USB external drive attached to the AE.

The disk itself seems to be fine with no errors upon using Disk Utility to verify, but the ~38GB TM sparsebundle will not mount so I can browse the band folders to search for the iPhoto library. I get a "no valid file system" error.

Would a file recovery utility such as Disk Warrior or Data Rescue do any good to recover the files from inside the bundle or is it hosed?