There are some groups that do "live steel" combats - where "live steel" is loosely defined as a weapon that could take an edge. They aren't edged, because that's just stupid in an amusement, but other than that, they are combat-capable weapons.
I don't know of any group in the US that does it with edged weapons. Nor do I know of any groups that make a competition out of it. People get seriously injured or killed in choreographed live steel performances, much less when they're actively trying to really hit each other.
Folks will argue to death about how sharp a "real" weapon needs to be. But, a 3+ foot long piece of steel, swung with vigor, will cleave flesh if it is no sharper than a butterknife.