Yes I believe that is true about the engine possibly overheating if it ran very long at all but usually it isn't running that long. What I do is fill the sea-chest to top with fresh water then have my wife start the given engine and immediately turn on the full force of the water. Usually within about 15 seconds the water level will fall to the level of the outlet of the sea chest to the engines and we then shut down the engine. I repeat this three or four times for each engine. A bit of wear and tear on the starting of the engine but I don't dare allow it to run without a full stream of water filling the engine sea water pump. I am guessing that as long as some water is traversing the engine impellers they are lubricated and ok but I am not sure so I have taken to the run/shut down routine.
I can tell you that if the water level falls too low in the sea-chest while flushing the Calpeda pump it becomes very noisy and starts to squeal. Therefore I do the same there with starting and stopping the AC a few times as soon as the flush water can't keep up.
Amel SM #335