Not necessarily. Ocean disposal of nuclear waste used to be an option, but was banned in 1993. Studies of disposal sites in use before then seem to indicate that any problems found were very local[0].
i'm sure that its safe to dump small amounts of radioactive material into the oceans, but if you start to build more reactors and dispose of all the waste into the ocean, the dilution will soon cease to be enough to offset a global ... disaster.
What does significantly radioactive mean? If I am a single individual, a single particle of Cesium or whatever could give me cancer. It's not an averages game when you're talking about real lives.
There's natural amounts of radiation that people are exposed to. Taking a commercial airline flight or handling a banana are good comparable measures - if it's less than those, it's not really worth worrying about.
