No, I ran the reservoir dry a few times during the operation, each for a few seconds. The pump makes interesting noises while this happens but I doubt it suffered any harm. In any case. I drove home last week for an hour after noticing there was a fluid leak and could hear the noise of the pump when I got home with an empty reservoir. I suggest flushing the system like I did today, starting with an absolutely full reservoir, but stopping when you have about 200mL of new fluid remaining and an empty reservoir. Then stop the engine, refit the return pipe and use the remaining 200mL to fill the reservoir. You will need an ***istant to start/stop the engine and turn the steering between runs.
My old fluid was filthy, the discharge into the coke bottle was dark brown with a frothy head on it, looked exactly like a pint of mild!