Do the ancient Japanese healing methods that Raizo performs on himself in the movie Ninja Assassin really work?
Sure. In the same way a placebo really work.
It's all about belief. If you believe you're receiving ancient healing, then yes it will probably work in the same way that a vitamin pill works for chronic pain or depression if your doctor convinces you that you're receiving cutting edge medication.
There are actual documented accounts of people who have been able to impale themselves and remove the impaling item without injury. I don't know of any who have been able to heal sword wounds got in battle inflicted by others.
If I knew of an actual ninja ability like this, I would hesitate to reveal it, out of due respectful fear... :-)