It depends on the RPM that you have set on the prop lever.
If the engine is not producing enough horses to turn the prop at that speed the prop will reduce pitch to keep up.
In practice you always set the prop to max RPM on approach.

Ok, so does the bottom of the green arc on the MAP gauge signify (normally about 15 inches) that below this the prop is going to fine pitch automarpticakky if it ain't there already ?

No, it is irrelevant. It just tells you the manifold pressure on a turbocharged engine and therefore the power being produced..
The prop knows nothing about MAP, it just understands RPM.

OK. I'm setting myself up as a target, but not me!

In the 182 towplane I fly, after takeoff, I bring the RPM back to 2300 rpm for noise abatement and leave it like that for the remainder of the flight, including the landing, again for noise considerations.

Now if I had to go around in an emergency, of course I would go to full fine, but I have determined (at altitude) that going around without changing the rpm and with those lovely barn-door (40 degree) flaps down, the rate of climb is more than adequate, even at DAs of 5000-6000'. I should confess at this point, that I am flying behind a P Ponk engine - 265 HP.