What happens if you rotate a stepper motor by hand while it is powered?
No, it won't cause any damage, at least in non-pathological cases where you're not exceeding some shaft or drive train mechanical limits and are applying a torque directly to the stepper shaft. 

A similar thing happens when you try to accelerate too fast and the motor loses steps. Nasty sound but not really a problem for the motor. The coil current is set by the driver in typical chopper drivers (or by a series resistor or just the power supply voltage and coil resistance) and will remain constant or drop a bit. 

Some drivers reduce the coil current to a fraction of the maximum driving current when the motor position is static (to reduce heating), and those will be even easier to turn.