Probably not.
First of all, a meltdown is exceedingly unlikely in a marine environment, where you can just submerge the entire reactor before it goes supercritical. A radiation spill underwater doesn’t get very far — its radius of effect is much, much smaller both than an oil spill and than a cloud of radioactive dust.
Second of all, modern reactors use designs based on pellet beds, which make it almost physically impossible to go supercritical.
As far as Chernobyl goes, it’s important not to confuse the plant’s integrity of design with its integrity of operation. The Chernobyl plant was, at its time, the most secure, fault-tolerant nuclear plant in the world. In fact, it was built with so many failsafes that its operational staffmembers decided that they weren’t needed at all, and spent most of their time goofing off and drinking. The day of the disaster, they decided to settle a bet to see how many failsafes they could deactivate and still avoid a meltdown. Turns out they all lost.