Is there a link between intelligence and mental disturbances? Is there a link between high intelligence or creativity, measured with currently valid psychometrics, such as IQ tests or tests of creativity and mental disorders like depression, anxiety, or bipolarity?
I like Mr Smitherson's consideration, which is indeed in the realm of possibilities. I haven't read a definitive study yet, I will search and return soon.

However, for further consideration to the question from a psychological/cognitive perception I posit the following:

Persons with abnormal, on the high scale of intelligence, would perhaps have more varied considerations when presented with a situation or when presented with a problem.

People with a higher IQ would normally think deeper into a problem. This would activate more brain cells, and drain the brain of the chemicals it uses to function. This would lead to imbalance.

The second consideration is that people who are more intelligent, would think about things further. To expand on that idea, since I am not the best at explaining stuff, I'll give an example: a person, of high IQ, is presented with information on global warming, a normal (for the sake of argument) person would take in the information and perhaps think "this isn't good" and leave it there. The person of higher IQ would thinking further about the implications, perhaps research and may find the situation hopeless.

Constant barrage of these situations may lead to lower moods and the elevated hopeless thinking lead to depression fueled by anxiety for the future.

This is what I would consider to be the cause behind any correlation between intelligence and mental illness in the form or depression/anxiety (these two conditions feed each other into a spiral)