Glycogen is a storage form of sugar found in the liver and in muscle. When you exercise your body breaks glycogen down to sugar and burns it. Actually, you burn a blend of fat and sugar. As the intensity of exercise increases the sugar fat ratio increases. Even at low intensities you consume some sugar for fuel. If the muscles start to run low on sugar the feeling of fatigue sets in. You absolutely need sugar (''fats burn in a carbohydrate flame'') so if the reserves dry up the body starts to degrade protein and turn that into sugar. Muscles are protein and its not good to be breaking them down for fuel. Especially on a hike.
All that just to say that on paper, Dr. Atkins and hiking is a bad mix. Eskimos however, had a low carb high protein diet and they survived ok. Nevertheless, a three day peakbagging fest in the Dacks would likely be pushing the envelope.