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.