If you need to ask this question, it's best if you seek the answer while keeping one eye on your gerbil. Cats are predators; gerbils are prey animals. Whether or not a cat will eat a gerbil depends on several factors, the least of which is the cat's appetite.
The Nature of the Cat
It's in a cat's nature to chase things that run. Cats learn from a very early age from their mothers how to hunt prey. The mother cat, usually referred to as the "queen," will bring home a mouse and watch as her kittens attempt to catch and kill it. Through trial and error, kittens learn to catch, and kill, their prey. Cats are impressive and intimidating killers. Because of the unique angle of their fangs, they are able to sever the spinal cord of their prey with one bite, a process called the "killing bite."
The Nature of the Gerbil
As a prey animal, it's in the gerbil's best interest to learn how to run away quickly from danger. But that's not their primary defense. Gerbils are friendly and curious animals, and this could be their undoing. A gerbil being introduced to a house cat may not immediately sense the danger, and will sniff at the cat in an effort to learn more about her. They are naturally friendly little animals. They stomp their feet when they sense danger in an effort to warn others of the danger. Once they realize they are in danger, they may dart, triggering the cat's prey instinct.
A Hungry Cat
A cat that is hungry will eat a gerbil if there is nothing else to eat. A house cat who is a companion animal with regular feedings is not as liable to kill a gerbil as a feral cat who is hungry. A house cat is being fed, and so she won't need to kill for food, so most likely she would not kill a pet gerbil. Cats, being natural predators, have a predatory instinct that has not been domesticated out of them. This is why they will jump out at you and attack your feet as you walk by, chase laser light toys, or chase, capture and carry a mouse made out of catnip and cloth. This predatory behavior may cause your cat to kill a gerbil, but not eat it. If you are feeding your cat well and she has plenty of toys to distract her from the gerbil, your gerbil is probably safe.
Don't Take Chances
So much depends on your cat's individuality and personality that it's difficult to answer this question in generalities. Use common sense if you have a gerbil, bird or other small pocket pet in your home. Never leave your cat alone with the gerbil without first ensuring that the cat cannot get into the room where the gerbil lives. The gerbil's cage or habitat may not afford much protection from a cat on a mission to liberate that gerbil and play a game of chase with him. It's far better to simply close the door to the room where the gerbil is being housed. Over time, you will understand your cat's personality and you'll know if your gerbil is safe or not. Until that time comes, watch your cat around the gerbil and stop any signs of play before it really starts.
- gerbille image by jÃ©rÃ´me caffin from Fotolia.com