Can radioactivity affect water?

Yes: By different means - it could be putting radioactive chemicals into the water or it could change the nature of the hydrogen atoms in the water. Most countries therefore have safety regulations around radioactivity and water quality. If there is any specific health concern re the possibility of radiation exposure please seek urgent medical attention from a doctor licensed in your area.

In short,...yes: Due to neutron activation, impurities or corrosion products like cobalt, sodium etc may get transmuted to activated products that produce radioactive radiation. In nuclear reactors, Cooling water is maintained at strict purity levels for plant use to avoid impurity activation. Material selection as well as corrosion mitigation procedures are followed at design stage to prevent corrosion products.