The armor on a battleship is mainly concentrated at the belt to prevent penetration of incoming shells. It's known as the "all or nothing" concept...vital spaces such as main machinery, gunfire control, and the gun turrets are heavily protected; other spaces such as crew berthing and mess decks have little or no protection at all.
I'm not aware of any studies done on an actual ramming. If the ramming was aimed at midships, there would be four layers of fuel tanks and void spaces to penetrate (each with about one inch thick steel plate) before you encountered the armor belt and, behind it, a large open main machinery space. I haven't been watching the series, but if the BB was crewed and active then Condition Zebra should have been set, with a very intensive watertight integrity maintained all the way up to the main deck. But, even if the BB was completely unmanned, there is still built-in watertight integrity up to the third deck, which should still be above the waterline if there is no other damage to the ship.
There is a great deal of kinetic energy in a ramming, but the BB's structure should do a better job of dissipating it than the bow of a DDG. Unless the DDG penetrated far enough in to split the actual keel (highly unlikely), the BB would not break in two. Even in a complete break-in-two situation, the two halves should not sink unless there was pre-existing battle damage such as a torpedo hit or similar. (Iowa-class BBs were designed to take a direct hit from a fairly large Japanese torpedo and survive...damaged, but survive.)
If the BB was crewed and armed, how did the DDG even get close enough to make ramming a factor? During my time on board, we even "sunk" a couple of aircraft carriers in war games...not sure I should share details here, but strange things can happen in the night watches. Particularly if you have a Spanish-speaking lieutenant from East L. A. on the bridge....
Disclaimer: All of the above is based on experience as a mid-grade enlisted sailor aboard a US Navy Iowa-class battleship.