The odds of seeing a stolen bike again are slim to none, as the police and even most thieves will view it as "just a bike."
Still, if you do see your bike and can use a coathanger to fish up your name in front of witnesses, it should help.
When I was a teenager, when dinosaurs roamed the earth, I worked as a mechanic at a bike shop and we'd sometimes see $600 bikes with rusted chains and flat tires brought in by kids for repair. Invariably, when we called their parents to ask where the bike came from, it was always a story like. "Johnnie bought it from Joey for $30. It's not stolen."
And the police didn't track stolen bikes, so there was nothing we could do beyond fixing the flat, greasing the chain, and watch it head out the door again.
The local police did start stamping serial numbers on the crank case bracket (metal frames) if you asked because bike theft was so rampant (it was a college town, so there were a lot of bikes), but I don't know if they followed up on it.
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