As always, it depends. Suppose, for a moment, that your prop is adjusted so that full fine is 2700 RPM, while full course is 2100 RPM. And the engine is idling at 1200 RPM, and the governor is set to full fine. The governor is then at the fine stops: It wants to go even finer to reduce the drag and increase the RPM but it can't.
Now adjust your MAP so that the engine makes, say 2400 RPM. At this stage the governor doesn't do anything, so it's still at the fine stops. But now pull the blue lever backwards. About halfway through that blue lever setting it passes the 2400 RPM setting. That will lift the governor off the fine stops. Pull the blue lever even further backwards and the engine will initially be making more RPMs than what the governor is set to. So the governor will change the blade pitch, setting them coarses, increasing the drag, until the RPM matches the governor setting, all the way to 2100 RPM.
However, do the same thing when the engine is idling at any speed below 2100 RPM and not a single thing will happen. The governor will simply not lift off the fine stops.
So it all depends on what your engine RPM is when idle, and what the full coarse stop is adjusted to.
Edited: Have to add that this assumes a normal single engine piston, where the failsafe (no oil pressure) is to go to the fine stops. If you're talking about a twin, with either autofeather or the ability to feather, or an aerobatics engine that defaults to full coarse, then things may be different.
Last edited by BackPacker; 16th Feb 2021 at 19:48.