Apparently, yes. According to study, discussed in an article in the Times of India, there appears to be a link between a person’s level of education and the quality of their sleep. The study of almost 40,000 Taiwanese adults found that:
…higher educational attainment improved women’s night time sleep quality while it had the opposite effect on educated men.
…rates of insomnia were found to be “still significantly higher” among women
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Studies have shown that children who get less than the recommended amount of sleep perform poorly on test scores than children who get the daily number of hours that they should according to their age. However, I don’t think just the quantity of sleep the child gets is important as much as the quality. Do they wak often with night terrors? This could definitely effect their ability to learn in school.