There are many reasons why an engine might fail markkal, loss of oil pressure is just one of them. In other failures, e.g. ignition, fuel malfunction, the prop would still be windmilling, and thus extracting energy from the air stream to drive the dead engine. In these cases, the propeller pitch is still controllable.
Am I right thinking that the statement above would be true for single-shaft turboprop engines but not for free turbine engines?
In a free turbine engine both turbine sections are not mechanically linked, so windmilling of the propeller would not drive the gas generator turbine which usually drives the gearbox to which the oil pump is geared to.
