Jeri,
I actually had that idea at one time -- seemed to make sense to me and I posted it here where it resulted in an interesting discussion. The disappointing upshot however, was that it would need a constant power source to work -- a source that would be combersome and hard to keep charged on a constant basis (I guess it requires more power than one might think).

If you could just get the thieves to plug in your instrument case wherever they take it.