A study by researchers at Kings College of London says they can, but I'm not convinced. Basically, the researchers took over 4,000 pairs of twins (both fraternal and identical) and tested them at both 4 and 14. They were asked to draw, and then their drawings were ranked based on factors such as the number of body parts. They were also given verbal and nonverbal intelligence tests at both ages. As expected, there was a moderate correlation between the "ranking" of the drawing and the intelligence score. Additionally, it seemed that identical twins (who share much of the same DNA) scored more similarly to each other than fraternal twins. Again, expected results, but I don't know that we can take any big conclusions from this. How can you really "rank" any drawing to be representative of intelligence? Is it really the number of body parts that should be counted, or aren't there other factors that are different among drawings that could be a better representation? Educators and researches often seem desperate to link intelligence level to genes in some way, and while genes are of course a factor, I'm still strongly of the opinion that there are other (more important!) factors in determining creativity and intelligence.