The Hiryuu school is, at its heart, a kenjutsu school. The only people who even get to see that aspect of it are family and other, hand-picked few. However, before you're permitted to so much as /touch/ a sword, you have to learn to fight unarmed and harness your fighting spirit.

So they could totally spar. But I dunno why Kotone would go to the kendo club. By chance?