I'm sure that a healthy diet will improve anybody's quality of life. However, I disagree that cutting out refined sugars and caffeine will necessarily lead to a situation where someone with BP will not require medication. You are probably citing Michael Ellsberg's article on Forbes (How I Overcame Bipolar II (and Saved My Own Life) - Forbes).

Personally I was skeptical of his argument, and also got the sense that he was a bit of an egomaniac.

In short, while I personally have cut back on refined sugars and caffeine, I think that Ellsberg's approach to go off medication completely can be dangerous. I don't recommend his article as a lifestyle -- it's just one man's story. Also, I second pretty much everything that Hamster has said above (except for the fact that cutting out caffeine might lead to a loss of valuable antioxidants -- this is true, although you can substitute for the lost antioxidants by eating a balanced, varied diet).