When the car overheated could it have done damage to the water pump causing it to go out three months later?

Hi. I need to know if these two things can be connected. My vehicle overheated when the cap was left off the radiator coolant bottle after having a service. I took it back to the garage and they had a look at it and said it was all okay, no damage done. Then three months later the water pump broke the bearings and gone. When the car overheated could it of done damage to water pump and then it broke three months later?