Yes...but in actuality very little due to the fact that it is heat caused by friction that does most of the dammage to impellers and your talking less then 60 rpm
..so unless as mentioned your bleeding an engine and laying on the starter for a long time I personally dont even worrie about it...
1 min or less total time in shorter 10 second spurts cranking up a cold blooded engine or low compression
engine is not going to vaporize all the water from the pump and harm the impeller, water is the lubricant...
Id rather replace an impeller then bend a rod from hydraulicking a motor
My procedure for a cold start is this if Im alone..I keep it closed..start the engine and dash below to open it...so Im getting a couple seconds at 3 to 4 hundred RPM
at the pump..which would translate into 30 to 40 compleat revolutions to the impeller before it got water if it took me 6 to 8 seconds to get below and open it.
If I have crew I have someone open it as soon as it fires from a cold start...of course most new or warm diesels should fire within a revolution or two so there is no issue anyway.
Just my Opinion... and FWIW..I change mine every two years in my boats not yearly because I cant use them that much yet..and I havent pulled a broken one yet.
Hope this helps