If the prop fails to coarsen, then at least an attempt has been made to
improve the glide ratio.
Any coarsening of the prop will do so in the event of total power loss.
I note in the Hartzell manual the statement "An operational check of the
governor and the propeller should be made during the run up".
No limitation on the extent of the check is identified in the manual I
have, and I imagine it is up to the individual to choose.
Equally, there appears no warning or advice to the effect that full
governor checks are detrimental, but I'll check the Textron manual to
see if it is mentioned.
My checklist for engine failure, or power loss requiring a forced
landing, includes the requirement to select full coarse on the prop.
The full coarse blade angle is 40.1 degrees, and sure is better than the
speed brake angle of 12.0 degrees.

Dom,

 

Righto!

 

Remembering various POHs, I use a drop of about 300 rpm (1800 --> 1500) to test the oil, prop, gov'nr and the B-nut that holds the actuating cable.  Since this test isn't done until the engine shows some internal warmth (oil at least 85F after the run up mag switch ck), I don't think any undue stress is placed on the engine.  Occasionally, when I have nothing better to do, I will slow down to best glide at some idle power setting and pull the prop coarse pitch - again, this should place no special stress on the engine including rapid cooling since the low air speed mediates that.