Basically anything you can do with an electric motor, you can do with a hydraulic motor. HP for HP, a hydraulic motor will be smaller than an electric motor. It can be a less efficient way to transfer power, but, that depends on how the system is setup.
Do some looking around here:
Surplus Center
This motor is just one example:
5.3 cu in PARKER MZG3AB876S1 HYD MOTOR
Relatively small but moves 37 horsepower at 1800 RPM! That is of course if you have the flow rate to back it up. You'd have to have a BIG accumulator for something like that, but say you only need it for 30 seconds to accelerate, that's not a ton of of flow. I've heard that UPS is trying this in new delivery trucks.
Many different motors are available in different price ranges, efficiency, size, pressure, etc.
That's how I'm going to do my hydraulic starter. A motor belted to the engine through an electric clutch. It could also assist with movement with a large enough motor. The electric starter will remain as a backup.
They also make hydraulic wheel motors, which would be FANTASTIC if they could be built into the front wheels of a RWD vehicle, but would create a ton of logistical problems.