I believe some models of Jeep/Chrysler used hydraulic cooling fan motors powered by the P/S pump due to the fact they are quieter.
I would speculate that the main reason for using a hydraulic motor is more to do with the high-temperature environment in which the fan motor must operate, especially if used on the back side of the radiator. At these temperatures, copper conductors get pretty lossy, and when running a 12V motor (drawing 20-30 amps), they start to really add up . . . in windings, commutators, brush leads, wiring, relay contacts, etc. And then you've got make up for those losses in power generation . . . and when a cooling fan is most important is when the vehicle isn't moving, hence engine speeds are low, and the alternator suffers from poor effeciency. In this application . . . hydraulic makes lots of sense.
But for a turntable, both air-vane and fluid-vane motors are far from vibration-free and cogless (go to an auto-body shop and listen to their air-vane-powered tools) . . . so there will be similar challanges as electric magnetic motors. Maybe an expanding-chamber screw-type armature fed by high-pressure hydraulic fluid? Then the problem is that you've got NO speed feedback, not even the fixed-frequency rotating magnetic field in an electric motor, and there's been disapproval voiced for a feedback speed control system.
Believe me, I'm not completely poo-poo'ing the idea, but rather will be extremely impressed if these challanges (and all of the others that I've not thought of) are able to be solved. And of course I'll want to read all about it, so do keep us posted.