This is just another Americanized myth. Green is worn on St. Patrick's day and it is a national colour, but there are no links between wearing it and being luckier. Indeed, there are also no links between wearing it and being lucky, either. I suppose it depends on what you believe.
However, if you don't wear green on St. Paddy's day, everyone around you is allowed to pinch/punch/kick/bite/cause physical harm to/shove you.