Over greasing can cause an issue with overheating the bearing because of lack of room for heat dissipation and the expansion of the warmed up grease causes the mess once the oil drops out of the soap..
Will it cause damage?? It will eventually, if the excess grease is flinging out of a seal, I would say that damage should be unlikely. It's all a crap shoot for the most part.

Also FWIW, the pump would need to come virtually all apart to replace the rear bearing seal.

Good luck!
GT