Would battleships have helped Taffy 3?

Would a couple of battleships backing Taffy 3 have changed the battle?

They could protect the carriers and buy launch time, but would probably absorb concentrated gunfire and torpedoes at severe human cost.

Heavy ships behind Taffy 3 would become the Japanese battle line's primary targets and could shield the escort carriers. That diversion might preserve flight decks and increase air attacks, but a battleship sinking would impose much greater casualties than losing a CVE. Concentrated gunfire and torpedo attacks would shift toward the capital ships as the most dangerous visible targets. The tradeoff is therefore tactical protection for the carriers at the price of exposing far larger crews and more valuable hulls.