Jim Stewart writes:

Does the curriculum specify engine-out training by shutting an
engine off completely?

[...] There's not much difference in drag between a prop in front
of an idling engine and a stopped engine, at least not on my plane.

Different story for a light twin. In Canada, getting the multiengine
rating requires a sign-off on having experienced at least one actual
in-flight engine shutdown (and one hopes, its restart). I haven't
done it on my own bird yet, but on the flight school's Aztec it was
surreal.

- FChE