In a nutshell, no. Here are some very good reasons why you need to consume fat on Atkins. First of all, fat is the mechanism that makes controlled carbohydrate weight loss work, and the Atkins Diet teaches you how to use fat to your advantage. When you are doing Atkins, fat is your friend, not only because it is satiating (keeps you full for longer) but because it slows down the release of glucose into the blood. By moderating blood sugar swings, fat reduces carbohydrate cravings. Dietary fat, in combination with controlled carbohydrate consumption, accelerates the burning of stored body fat. When your body uses fat, rather than glucose for fuel, the metabolic process is called lipolysis. Eating fat fuels a fat-burning metabolism and accelerates the burning of fat, both dietary (from the foods you eat) and stored (from the excess around your waist, hips and other areas).
However, you do want to eat good fat. Natural, healthy fat is found in olives and olive oil, avocado, seeds, nuts, seed and nut oils and butters, and oily fish such as salmon, sardines and mackerel and butter. Saturated fat, found in meats, butter and coconut oil, poses no health risk when your carb intake is low enough, and you are burning fat for fuel. In fact, you will burn both dietary and body for energy.
Three types of fats (saturated, monounsaturated and polyunsaturated fats) are necessary and important to human health, and they should be incorporated into your diet in a balanced proportion. Saturated fat, particularly in the early phases of Atkins when carbohydrate intake is low, is not dangerous to human health. On the contrary, when balanced with mono- and polyunsaturated fats in a controlled carbohydrate dietary environment, saturated fat may actually have real and measurable benefits in a number of different arenas.
When you are no longer in a primarily fat-burning mode, it may be prudent to curtail the amount of total fat so you are not taking in an enormous amount of calories. Your dietary pattern should play seesaw with carbs and fat, while your protein intake remains constant. As long as you are consuming 50 grams of Net Carbs or less, there is no need to adjust fat intake. What you want to avoid is a high-fat AND a high-carbohydrate combination.
The kinds of fat you should avoid are chemically altered, processed hydrogenated oils, also known as trans fats. Look for cold-pressed or expeller-pressed oils, and store them in a dark, cool place to keep them from going rancid or oxidizing. High heat changes the molecular structure of the cell and will transform even a good fat into a bad fat, so be sure not to burn oil or allow it to smoke while cooking.
If you try to do your own low-fat version of Atkins, you will not only be hungry, but you also will not achieve the same weight loss results of people who consume healthy fats.