While there is no requirement anywhere in the PTS or regs that requires a full shut down of an engine during training, personally, I believe it is good training for the student. But it must be under controlled conditions. Lots of altitude, light aircraft and CLOSE to the airport. There are too many things that can go wrong. But I have also worked with pilots who have never seen a prop feathered before. The look on their faces is beyond priceless.
To answer the other part of the question, I would declare as you couldn't get the engine restarted. Therefore you had a 'real' engine failure.
To answer the other part of the question, I would declare as you couldn't get the engine restarted. Therefore you had a 'real' engine failure.