Yes and no, the ship and crew might have survived. But the steel wasn't thick enough to block all the radiation. Moreover traditional ship design up until that point didn't handle Nuclear Biological, and Chemical threats well. They weren't really designed to be completely sealed. It's important to recognize that the assumption that the next war would be atomic killed a lot of technology paths because the people with the money assumed it was a waste of time to continue in those directions. By the time the military started to re-explore those paths the tech had languished. It's why the Iowas went back to sea with the Mk8 fire control computer, a completely analog computer. Because nobody had really bothered to build a better one for large caliber shells since WWII.
But it's important to note that before the Iowas were given their final retirements into museum ships the Navy made sure to basically document everything they could about firing large caliber guns. Because when they initially pulled them out of mothballs in the 1980s they were woefully inaccurate, but by the time they were decommissioned for the final time they could hit a proverbial fly on a flag pole (allegedly).
The other part of it was that the Soviet Union didn't really have a surface fleet to really speak of. They invested heavily in submarines, so consequently the US Navy focused heavily on ASW. So... nobody really knows how 16" of modern armor would fair against modern weapons, it's literally never been tried. Whereas you can find pictures from way back when they were testing guns, of how various shells fared against various thicknesses and types of armor.
Long story short: We've forgotten most of what we knew about surface warfare, and we're starting to forget what we knew about shipbuilding and design. The US has outsourced all it's naval architecture and shipbuilding so long that the necessary skills are either all retired or lost.