If Bragg would had the back bone to take Fort Pickens at Pensacola prior to the fall of New Orleans...

1. New Orleans and the lower Mississippi would not have fallen.
2. The Union naval block-aid would have been a joke.

To win the war the South had to protect the Gulf Coast and all the rivers accesses-- [who ever controls the Gulf Coast controls the interior of the country] War of 1812 military rule.

To defeat the blockade the South had to deny coaling/fueling stations within the Gulf of Mexico to the Union Navy. Fort Pickens, and then Sand Island Mississippi, and then New Orleans gave the Union Navy freedom to blockade the entire coast from Texas to Keywest..

By giving up Fort Pickens and later Pensacola, the South had no chance to win.