Trident gum is a sugarless gum that is safe to consume. There are no calories in trident gum, so it is a good choice for people who are watching their weight. Trident gum is also a good choice for people who have diabetes or other conditions that require them to limit their sugar intake.yes, you can eat trident gum. However, trident gum is not intended to be eaten and it is not nutritionally complete. Trident gum may pose a choking hazard and it is recommended that you consult your physician before eating trident gum.