Do different boilers require different gearboxes?

Would ships with different boiler installations all need different gearboxes?

No; the gearboxes are associated with the turbines, but piping, fuel supplies and internal arrangements would differ.

A different boiler installation does not automatically require a different gearbox because the gearbox belongs with the turbine system. It does require a different arrangement of boilers, piping and fuel supplies. Steam must reach the turbines from machinery placed differently inside each ship. Those requirements can alter much of the internal layout even when sister ships look alike outside.