Can a human being live without any carbohydrates?
The Atkins diet is based on that. Without carb intake, however, the citric acid cycle (CAC) eventually basically stops and proteins will be utilized to be converted to carb intermediates to feed the CAC. Progressive and strict use of the Atkins diet will eventually kill you as the CAC is essential to life. 

The idea behind Atkins is that fats will be used to feed the CAC, and that will happen until the carbohydrates that keep the cycle running are depleted. At that point one will develop ketosis and the CAC stops, and with it the production of ATP. Note that fatty acids can be fed into the CAC, but are not sufficient to keep it running; fats burn on a fire of carbs.