According to Kids Health, the short answer is no, drinking soda does not stunt children's growth. However, consuming beverages with large amounts of sugar and caffeine can have negative health consequences.
Prevention Magazine explains that caffeine can cause transient increases in heart rate and blood pressure. If consumed too close to bedtime, caffeine can cause insomnia. More worrisome than caffeine is the sugar content of non-diet sodas. Kids Health states that excess dietary sugar leads to tooth decay and worse still, obesity. The American Heart Association agrees that it increases a person's risk of developing obesity and diabetes.
Caffeine and sugar may also worsen hyperactivity in children with Attention Deficit Hyperactivity Disorder, or ADHD. Finally, studies suggest that people who drink beverages high in phosphates, such as colas, are at a higher risk for developing kidney stones.