Try it. With the throttle closed in a glide, pull the prop control all the way to course pitch. You will be amazed at the reduction in sink rate. Do push it forward again on short final in case you do need the power to be available as it will take a period of time to "spool up" again.
I attempted the test on Sunday but started too late in the day. Tried again this morning with takeoff about 5:15 am.
Before flight I verified full governor stop to stop control from the front cockpit prop lever. Each test descent was with throttle on the idle stop and with autopilot engaged in Heading and IAS hold modes. IAS target was 70 mph which is close to best glide speed at max gross. Actual aircraft weight was well below max gross so actual best glide speed would have been lower.
Each test point started with a climb to 4,500. Aircraft was slowed to 70 IAS, throttle was retarded to idle stop and prop was set as required for the test point. The descent to 4,000ft was used to stabilize on point. The descent rate was evaluated between 4,000 ft and 3,000 ft. The first 3 runs were reasonably stable but the sun was up before the test was completed and the later runs were less stable.
The test runs were as follows:
1. West heading prop fine
2. East heading prop fine
3. West heading prop coarse
4. East heading prop coarse
5. East heading prop coarse
6. West heading prop coarse
Cockpit observation showed approx 900 fpm for each of the test runs.
An additional test point was hand flown with throttle idle, 70 mph IAS, and prop lever cycled several times between the fine and coarse stops. There was no change in noise, rpm, sink rate, or pitch feel.
Quick look data shows no obvious change in sink rate for the evaluated throttle and propeller settings. Data for the first 5 descents attached.