We need to separate this question into two components. These aspects are first, would the battery suffer physical damage. Then secondly, would it discharge in water? The first question is dead simple. Since manufacturers go to great lengths to prevent their products leaking, their batteries survive a flood quite easily because the water can’t get in.
So Would the Charge in Starter Batteries Survive a Flood?

Once again, there are two possibilities to the answer. Pure water is an extremely weak conductor of the electricity we store in batteries. Please note this does not apply to the alternating current we get from the electricity grid. If connecting your boat to a wharf-side supply, take extra care not to drop live cables in the water.
However, your battery should not discharge if you tip it off the deck into a lake, river or stream. That is because pure fresh water has so few ions in it, it is hardly capable of conducting electricity between battery terminals. If the battery was on load at the time, say powering your cabin lights you might not even see a flicker. Electricity is lazy because it follows the path of least resistance. That’s how batteries survive a flood.
However, the Same is Not True of Salt and Sea Water

Over time, any metallic components corrode in seawater. Even the Titanic is gradually decaying. A disconnected battery will gradually discharge in seawater because this has more ions than fresh.
But, this resistance is higher than copper wire. Hence the electricity in a connected battery will continue to supply the circuit pretty much as if it were on dry land. Therefore it is generally not a problem if a starter battery is splashed while driving through a puddle.
We end with an interesting insurance angle. If a battery suffers water damage, many insurance policies would not cover it (although they might cover consequential loss). If you own a hybrid or electric car, call you broker and ask them what would happen if your battery did not survive a flood.
Related
What Happens In A Battery Discharge Cycle?
How Leak-Proof Batteries (Almost) Happened
Image Preview: Sunk Canal Boat