I can't remeber the maths now - it was a long time ago but I do remember in Mechanical Engineering at Uni having to do two calculations about gyro effects.
One was how much a prop aircraft would pitch in a turn due to precession.
The other on was a frigate with a gas turbine with a shaft length of x, turning at y rpm while the ship was tuning at z deg/s and having to calcualate the forces in the shaft and on the bearings.
The forces are definately there.
haven't we left out the very critical parameter germain to fan engine discussions like diameter or polar moment of inertia
Just as an aside, the bearings and bearing supports in a gas turbine can take some pretty high loads for a short time, but the nut holding the bearings and shaft together has a real difficult time when the gyro load precesses and tries to unscrew it like a tyre iron releasing the bead from a tyre rim