Can I pose a hypotetical question

We were discussing Engine failures in single engine aircraft with a constant
speed propeller..
Not catastrophic but more like fuel starvation types, where the prop keeps
windmilling..

The question is on getting the maximum gliding distance from the windmilling
prop..

It is assumed that a higher pitch/lower r.p.m. would give reduced drag:
hence maximum gliding distance..

The question is: Would a windmilling prop generate sufficient oil pressure
to maintain control of the propeller
and what r.p.m. would one expect from this scenario?