I may be wrong but i dont think on sf you will go into ketosis due to the carbs in milk and the other foods.I know on diets like cambridge that to get to ketosis you cant have any food or milk and i was once told that even chewing gum can bring you out of Ketosis so i really doubt that you can.
I have never done the diet myself so i could well be wrong but i'm sure someone who knows for sure will give u a more informed answer.