Can the power steering be damaged if turned with pump not running?
 

w140 with SPS
Can the power steering be damaged if turned with pump not running?
Turned more than a few times that is... don't know how many turns and for how long.

So is it possible to damage the steering box?

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.

I drove my '77 240D from San Diego to Carson city with no power steering belt once. No damage.

As a side note, if you have to drive without the PS pump turning, drain the fluid out. This way you are not displacing fluid every time you turn the wheel.