The answer is: sort of. One of the ingredients in coke is sodium bicarbonate, or baking soda. This is an alkaline substance, and therefore can help balance the pH level in the stomach. So, if the cause of the nausea has to do with too much acid in the stomach, or acid rising from the stomach into the esophagus, coke can have a relieving effect on the condition.
However, coke also contains caffeine, which relaxes the border between the stomach and the esophagus, as well as increases stomach acid production, two actions which can worsen the condition. Because the caffeine takes more time to take effect, the baking soda in the coke may provide a temporary relief before the problem is worsened. Doctors recommend letting the soda go flat before drinking, or adding a pinch of salt over the top.