It's certainly a long string of if's.

What exactly could the CSA do differently with Baton Rouge if they retook it? The Federals withdrew from it after the battle anyway so the CSA regained it even after losing the battle. Unless the CSA leveled the city it would be vulnerable to attack from the rear, and from the river it appears that it was highly vulnerable anyway. The CSA did not have the shipbuilding and engine/boiler building capacity left on the Mississippi to defend Baton Rouge from the water. Later events showed Port Hudson to have been a far more logical and defensible stretch for the CSA. Port Hudson tied up far more Yanks and cost them more dearly than any short term capitulation of Baton Rouge would have done.

Williams' Division was pretty well used up by the canal work, so their capture would have had far less impact than that of bagging a healthy division. Strategically, it was far better for the North to have the CSA banging up their own veteran divisions vs. an infirm Federal division. (This was one of the reasons that the exchange cartel was halted late in the war.)

Baton Rouge seems to have been an illogical action, a vanity play. It was a waste of CSA/CSN resources with little potential strategic gain, but great risk. If the CSA had instead used the Arkansas to patrol between Vicksburg and Port Hudson so that it had a strong defensive position/shelter on both ends then it might have achieved more.