If your engine has stopped for a reason other than oil pressure failure/internal mechanical failure, you should expect that a windmilling engine will provide enough oil pressure to move the pitch to coarse, if it is that type of propeller. Note that if the engine is allowed to windmill to a stop, you may no longer be able to select coarse or feather pitch, due to fine pitch blade latches.
Selecting coarse pitch will have favourable affect on gliding. For one of my planes, this is vital, as the power off (engine running or not) fine pitch glide is very steep, and selecting full coarse completely changes the glide characteristics to be entirely fine.
Note that in the case of a failed engine which is windmilling, throttle position will not affect how the engine operates if it is not creating any power.