There is some correlation but it depends on the test, a lot of tests rely too heavily on experience. For example, there use to be a question with a picture of a bike asking what was missing. Obviously you could be the smartest person in the world but if you never rode a bike you would have a hard time answering that question.
In my undergraduate opinion I think the only questions that should ever be on IQ tests are those "what comes next in the pattern?" questions, because those don't rely very heavily on cultural experience.