(Dietary) Ketosis is only partially about low carbs, the other major part of the equation is high fat. With Atkins (like paleo diets) you might get the right amount of fat intake to enter into Ketosis, but it’s more likely you will be consuming to much lean protein and you will continue using glucose as your primary fuel source.
It did indeed induce ketogenesis, in fact regular testing of urine for presence of ketone bodies was how one monitored whether their carb intake was appropriate