I would assume it would make considerable noise, especially if the broken impeller made contact with the housing internally. The excess movement of the fractured blade(s) against the coolant would probably emit some sort of muffled whirring noise that would be louder than normal.
I heard a seized water pump make a sort of high-pitched "chirping sound".
Typically when the coolant pump goes, it blows a seal, and the result is a slow leak through the weep hole. Can't see this from the coolant pump because of the tight confines, but the resultant coolant loss as evidenced by the pool directly underneath the car is a sure sign of coolant pump failure.
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car