A prop at fine pitch creates more drag than a prop at coarse pitch. Pulling a non feathering constant speed prop into full coarse will extend your glide in an aircraft like an Arrow or C182 etc.
Having a prop go to coarse pitch when power is reduced or lost means you no longer have a constant speed prop. A constant speed prop reduces blade angle, i.e. goes to a finer pitch when power is reduced in order to maintain the set RPM. Likewise when power is increased the prop goes to a coarser pitch to absorb more power and maintain the set RPM.
The latches on a feathering prop only drop into place at RPM below about 1300 to1400 RPM, which on an engine with a constant speed prop is a pretty low power setting. Even at idle power and any airspeed above around 80 knots you'll find the RPM will be at least 1400 RPM.
Remember RPM hardly even changes when an engines fails, the constant speed prop reduces blade angle and RPM pretty well stays the same as before the engine failure. Even manifold pressure remains pretty well constant after a failure. Try "failing" an engine sometime at a safe altitude by pulling the mixture to Idle Cut Off, you will see what I mean. I'm primarily talking about a twin here as the speed remains relatively high and the forward speed keeps the failed engine turning. I would expect a similar situation for a single too at a normal glide speed.
Under pretty well all conditions with an engine failure there is no rush to feather the prop for fear of it not feathering due to the latches operating, at least with a metal prop, some of the lighter composite props may act differently.