No doubt a starship would be able to go underwater without drowning its occupants, but I would be willing to bet that many, many components would respond poorly to submersion in water (nevermind saltwater), particularly engines and sensitive sensory modules, none of which are likely intended for that. I guess as long as your shields stayed up you'd be OK, but you'd be looking at potentially catastrophic module failure once they dropped.
That would make underwater combat very interesting.
Let's do it.
Although it occurs to me that all the air trapped in your shields would make you very buoyant.