The Russians have been. I haven't heard of giant plumes of radioactive ocean water.
There would be no need for Yucca Mountain.
Big difference between 1 carrier reactor and waste from all the civilian reactors from the last 50 years.
None of these rabbit trails address the issue that once Americans see their aircraft carriers on the downside of sinking/burning/radiating or whatever, they will lose stomach for the fight.
That's what the Vietnamese perceived was the American weakness and they exploited it. The Chinese are likely to choose the same type of strategy. And when they see a weakness or a downside for America, they will augment whatever disaster scenario it is. They don't have to have a top notch military strategy, just one that would bring thousands of casualties, even if it means millions of casualties for their side.
Maybe the sea can absorb the radiation damage, maybe it can't. Maybe the Marianas are a better place to put our nuclear garbage than Yucca Mountain. It doesn't matter in the context of this discussion. What matters is what Americans will THINK when they see horrible scenes of death/destruction/defeat on CNN and then whether they'll find the resolve to spill more blood for Taiwanese independence. My sense is that Americans won't, and I believe the Chinese are tuned to that as well. It does not bode well for Taiwanese democracy & independence.