I live in a condo building that has one water heater for all 20 units
and a recirculating pump to keep the water warm to all units. I didn't
know we had a recirc. pump and was going to have some plumbing work
done. The plumber wouldn't do the work unless he could verify whether
we had one and if so, turn it off before turning off the building's
main water. He said that turning off the water without turning off the
pump would damage the pump. However, thinking back on previous
emergencies other people have had in the building, the water has been
shut off in the past, sometimes for several hours, without damaging
the pump.

Can turning off the water damage a recirculating pump?