I've seen some katas that work that way. I've also seen some that were very stylized, and would probably not work well if done in a fight, but still required some skill to perform.
A kata is an exercise routine (or a 'warmup') that is particular to a certain skill level in a certain martial art. At the higher levels, it becomes unique to the martial artist, as well. While it could be useful as image training, similar to shadow boxing, the primary purpose is more of a general workout, improvement of motor skills, and to identify and demonstrate your skill level.
The easiest source I can think of to see some weird ones would be to look at the 'Weapon Practice' videos in Soul Caliber 2, where you can unlock each character doing a kata. Mitsurugi, Taki, Sung Mina and the new Hwang clone all do some fairly traditional stuff, while everyone else has something to suit their style.
BTW, what we do in CoH looks more like a beginner's Tai Chi workout, which is also a kata, but a very weak one.
