According to the law, you have to register with the local authorities. Technically a law was broken, unlikely it will be used against you unless they make it a prerogative.
Yes, I believe I was registered. Airbnb takes a copy of my (and any fellow friends staying with me) passport and does a few extra checks compared to stays I've had in Australia. Having said that I was staying in a pseudo-serviced apartment so it may have just been a normal hotel that was advertising on Airbnb.