You're still going to use the calories taken in (as proteins and fats) before you start burning your fat stores for energy. If you're losing weight on the Atkins diet it is because you are burning more calories than you are taking in. Again, the calories in fats and proteins are no different than carbohydrates, except that carbs are quickly digested and the energy liberated goes to refill muscle and liver glycogen stores first. If the carbs satisfy the body's energy needs then the calories from fats and proteins will get stored as fat. If you're not eating carbs then the proteins and fats will be used when ingested, but they are much slower to be digested, so in the absence of quick glycogen then the body will get the energy needed to digest the fats and proteins from whatever sources it has available, including your fat stores. But if the body gets what it needs from fat and the ingested calories aren't needed, they will be stored as fat. So you're back to the original problem of calories in must equal calories out or you won't lose weight.

MNS