No. A species-appropriate diet for cats and dogs consists of raw meat, bones and organs, from a variety of prey species (to ensure nutritional balance), minimally processed, with nothing else added. It is high in protein, with moderate fat, and low carbohydrate. Grain-free diets are not low in carbohydrates.
Studies in macro-nutrient selection have shown that dogs and cats have an innate drive to consume a diet that is not more than 12% carbohydrate (and the bulk of those carbohydrates would come from the pre-digested stomach contents of herbivorous prey - tripe).
Grain-free diets are still high carbohydrate diets, which pose issues for pets. They simply take out the grains, and replace them with other carbohydrates. Renowned animal nutritionist, Dr Richard Patton states that:
"Grain Free" is a descriptor for pet food intended to mean, no corn, soy, wheat, barley or oats. This is the epitome of false security and I don't know who to criticise more loudly, the consumer who buys it or the marketer who pushes it."
Dr Karen Becker writes about grain-free diets in detail here.
Here at Raw Essentials we are also critical of the marketing behind grain-free food. The absence of specific grains does nothing to lessen the carbohydrate load of these foods - as pet owners flood to these foods in the hope of remedying allergies and obesity, things don't get any better for today's kibble fed pets. Here's a light-hearted look at how this sort of marketing works.