Kenpachi's sword is all busted up because he doesn't know how to tap into it's abilities. Normally, when a zanpakutou is damaged, it's able to heal itself like Ichigo's in his fight vs Kenpachi when it was cut in half. He doesn't even know its name, so it can't heal itself, much less be a shikai.

Even if it were a shikai, what difference would it make? All it does is cut like a normal sword.