If you think that police will actually search for your stolen guitar, I have bad news for you: Santa doesn't exist.
The only situation in which police might get your guitar back is when they do a raid on organized crime. The chances for that are very slim, as most stolen guitars are probably theft of opportunity.
Just saying: Nobody visits a church for the slim chance of stealing something valuable. It's probably just a kid who saw a deserted stage and used the opportunity to enhance his pocket money. Let that be a lesson, folks: never leave your stuff unattended!
If you happen to find your guitar on ebay or craigslist a common strategy would be to purchase your guitar back (as much as it hurts to pay twice for the same guitar ... justice always comes at a price), then sue the vendor after having physical evidence. If you get paid for your gigs, you can even sue him for loss of earnings. But you will almost always come out at a loss. I never heard of any cases where legal actions against gear thieves broke even.