The function of compact 8-inch carrier turrets

Were the small 8-inch carrier turrets fully functional, or was their rate of fire restricted?

They were fully functional, with no rate restriction identified, although they were not considered good turret designs.

The compact carrier turrets raised in the question are described as fully functional. Their rate of fire is not said to have been restricted. They are nevertheless judged poor turret designs, reinforcing the objection to putting them aboard an aircraft carrier.