Ketosis is a metabolic state. It is the process by which your body converts fat into energy. Anytime you lose weight you have been in ketosis... Every night when you sleep your body goes into ketosis.
What people commonly refer to as a ketogenic diet, is just a shorthand way of saying, eating food that maintains your fat burning preference.
So this yogurt diet, will absolutely put you in ketosis, for no other reason than you're at a caloric deficit per day.
I am not aware of any reason your body would cannibalize your muscles when you have sufficient protein. People often do month-long fasts, as long as they maintain their metabolic rate/activites, they don't lose significant muscle mass. But this is a function of your stored energy, so if you don't have enough fat to make up for your metabolic deficit, that energy will have to come from somewhere as a priority to keep your brain alive. Don't put your body in that position. The science around fasting, is highly contentious, so you're going to get wildly different viewpoints on this.
