This looks like the magnetic amplifier concept. If your transformer had a sharper knee in its saturation curve, then you might be able to adjust the action to make an imperfect diode. It would have no voltage threshold (whereas diodes do have a voltage threshold).
Here is a webpage which talks about a magnetic amplifier being able to obtain an intermediate output voltage which would not normally be available using diodes.
**broken link removed**
"Magnetic Amplifiers in a Nutshell...Now, why do you see these mag amps in power supplies? Because they need 3.3V, but are only wound for 5 and 12V. What they do is this: if you half-wave rectify the 5V winding and filter it, you'll get half, or 2.5V, which is too little. If you full wave rectify, of course, you get 5V, which is too much. So this mag amp inductor goes in series with one leg, so when it's "out of circuit" (biased to full inductance), the output is essentially half-wave rectified, so it will make 2.5V."