Let's say we put a human in a closed chamber which is going around a certain point at distance d from its center of mass at some angular velocity w. The centrifugal force on a human will be w squared over r times his mass. Is there any difference if the cause of this rotation is precession of a gyroscope connected to the chamber?
A reference frame rotating at the rate of a precessing gyroscope is still a rotating reference frame. It is not inertial. All of the usual effects in a rotating reference frame will be present including the usual centrifugal force.