Is it true that the Atkins diet is a low-calorie diet?

No, it’s not true! Atkins isn’t about counting calories. While doing Atkins you can eat fewer calories as a result of being less hungry and less obsessed with food.
Atkins counts grams of carbohydrates instead of calories. At the beginning of Induction diet you are allowed 20 grams of carbs, gradually adding them in 5-gram increments as you progress from Ongoing Weight Loss to Pre Maintenance, and finally to the Lifetime Maintenance phase of Atkins.