Generally no, for one specific poorly designed car yes.

When the wheel is turned, fluid is displaced from the steering rack / box and it ends up in the pump reservoir. If there is an overfill situation or a low free space reservoir, fluid can be displaced out the vent. My 1984 Ford Bronco will dump fluid if I turned the wheel with the engine off.

The specific car I've seen damage occur was on a 1997 ish Pontiac Grand Prix, these used a sealed power steering cap and this particular car may of had an over filled condition. The drive belt broke, car was driven, power steering return hose popped off the barb. ( these are attached with a hose clamp since it is a no pressure return hose. )

If you car has a non vented system, I'd open the cap to release pressure and then once the engine had run / shut off, open int again to release vacuum.