2009 Toyota Corolla

Yes they can, if the water pump is extremely worn it will throw off the belt sometimes causing it to become shredded in the other pulleys, The belt itself wont break the pump unless its plastic.

Is it possible to detect a bad water pump? My car was at Toyota 4 days before to have a recall fix and they did a multi point inspection and said the car was perfect.

sometimes you can hear them other times there quiet and show no signs especially with the belt holding the pump together thats about to fail so to answer your question yes but also no because its not part of the inspection they will usually check the belt and if there are no signs of odd wear it can easily be overlooked.

Where is bod location 2009 Toyota Corolla