Continued Low Level Exposure?

Is it possible that we'll actually continue to see elevated levels of radionuclides in West Coast rain as fallout in the Pacific is absorbed into storm systems?

Just trying to understand how some of the radionuclides like Ce-137 will behave once released into the ocean. I get that the ocean has enormous diluative powers, but trying to see if there are other pathways that this stuff might end up affecting us here in the longer term. The more Ce-137 introduced into the food chain, the greater potential harm to public health/safety as the low doses add up, right?