Could it happen yes possibly.

Could it work? Actually yes maybe not completely but most people would wait until that time to commit a crime if they could get away with it. It would cut down on random crimes and most others days would be safer on average.

Would I participate? It depends on the rules covering it. I wouldn't if rape was allowed, or if it was the armed versus the unarmed, or if people in hospitals, children, or those too disabled to defend themselves were allowed. I also wouldn't if it allowed explosives.

Now if everyone was armed (which seeing how gun prices would probably drop they should be able to afford to be), none of the defenseless were able to be targeted, and if rapes weren't allowed then I'd consider it. Personally I'd use it to kill off known neo-nazis, hate group members, sex offenders, and gang members etc.