Gun calibres for defending ships against drones

Would battleship secondary guns be useful against naval and aerial drones?

A layered defence is suggested: 6-inch guns at long range, 3-inch guns at medium range and 40 mm weapons close in.

Secondary and tertiary guns could help counter drones, with calibres chosen for different engagement distances. A 6-inch weapon is suggested for very long-range attacks. A 3-inch gun would supply a medium-range layer and a 40 mm weapon the close defence. Numerous cheap drones make ammunition economy important, so each gun should achieve a kill with as few shots as possible.