Keep in mind we've also blown up 500+ nuclear bombs including almost 10 underwater. Not a great idea in hindsight, but overall we didn't experience any major problems as a result.
Seems like even in the worst and extremely unlikely scenario of full detonation, we'd still be fine.
The difference is that those tests were done on or near land, the fallout settled either on land or in shallow water, close to marine life.
The explosions which happened in deep water (Wigwam in 1955 for instance) had practically zero lasting effects beyond radioactive steam entering the atmosphere.
The scale is a little different though. Say a 300MW submarine reactor runs for 10 years, the energy produced is about 20 megatons. The energy in a bomb might be 400 kt, half of it from fission, so the reactor will contain a hundred times more spent fuel.
Seems like even in the worst and extremely unlikely scenario of full detonation, we'd still be fine.