I voted no because I think it would do no good, and adds to the red-tape that we all must deal with in our daily lives.
However; I remember when I was a kid (30 years ago), that we were encouraged to "license" our bicycles. We would take the bicycle to the local police station and pay a small fee. The police department would give you a sticker to place on the bike. The sticker has a registration number that could be used to return the bike to you if it were lost or stolen. I think this practice went the way of fire alarm boxes at the end of the block, soda fountains and 10-speeds.