In general it depends on the pump.
It will normally run a little faster backwards than forwards, so it needs to be checked that safe speeds are not exceeded. Also some shaft seals are unidirectional so this also needs to be checked.
I have recently put in a 300kW, 3000rpm multistage booster pump deliberately with no discharge check valve.
I calculated the no load reverse speed to be 3400rpm. The manufacturer said the pump assembly (pump, motor, coupling, seal) can stand in excess of 4000rpm, so we will see.
The practice of permitting reverse rotation, is reported by Stepanoff as being common with deepwell (multistage) pumps with no mechanical damage arising.
Cheers
Steve