Pair of scissors to remove the cover or go in near the lock with some small bolt cutters. The fabric hinders rotorary cutters, but attacking the chain near the lock or cutting the fabric would have it defeated pretty quickly. Thats an easily cuttable chain.
It's a good idea, but probably not secure enough for my purposes.
Agree about the lock area, but it's a promising start, and attaching to the cross bar is a great idea.