If by "radioactive" you mean "ever emits radiation" then yes, a small amount of radioactive water can dilute into a large volume of still-radioactive water.
By if you use that definition you yourself would be considered "radioactive" as you are always walking around carrying quite a few radioactive isotopes, including Carbon-14 (as made famous by "carbon dating" from geology) and Potassium-40.
As pdonis notes, radioactive contaminants dilute just as well as any other contaminant in water. Assuming it more-or-less evenly mixes within the Pacific Ocean, you could essentially dump all of Fukushima into that ocean and not see large changes in overall ocean radioactivity.
By if you use that definition you yourself would be considered "radioactive" as you are always walking around carrying quite a few radioactive isotopes, including Carbon-14 (as made famous by "carbon dating" from geology) and Potassium-40.
As pdonis notes, radioactive contaminants dilute just as well as any other contaminant in water. Assuming it more-or-less evenly mixes within the Pacific Ocean, you could essentially dump all of Fukushima into that ocean and not see large changes in overall ocean radioactivity.