Is the Katana any good?

Yes it is a good weapon choice, and very strong and killing groups of closeby zombies, but it's not so great at killing the bosses because of the way the skill works in terms of the direction it hits when you are moving.

So it seems you always have to be moving towards the boss or directly away from it, and be closeby for it to hit.

A better option is the Kunai and it's Shuriken evolution, this will hit the boss from wherever you are. It's also very strong at hitting individual zombies, and it's Shuriken evolution will hit many zombies at the same time.

Kunai is much better as its autoaim and the evo is much more powerful; it's on the same scale as the gatling gun but with autoaim.