FWIW
Noll on Pearce, 'Pensacola during the Civil War: A Thorn in the Side
Union troops stayed in control of the city for the remainder of the war, even though troops were evacuated to surrounding forts in March 1863. Sporadic raids and skirmishes took place in the vicinity of Pensacola, but no major battles occurred. Union soldiers periodically marched into the surrounding countryside, destroying and confiscating "agricultural products and farm animals, timber and lumber, and household furnishings" (p. 237). Pensacola became an important port city for ships of the Northern blockade squadrons, as its harbor and navy yard provided docking, coaling, and refitting stations for Union vessels. Though few battles occurred in the region, Pearce concludes that the strong Union presence there was a factor in the overall Northern victory. In order to block Union incursions from the Pensacola enclave, "a fairly large troop concentration that could have been used in other places in the Confederacy to better advantage had to be maintained in the Pensacola military district" (p. 237). Part of the plan to stretch the Confederacy thin and force it to allocate scarce resources over a wide geographic area, the Union occupation of Pensacola was a successful, yet unappreciated, piece of the larger Union strategy.
IMHO without Pensacola in Union hands, the Union could not have blockaded the Gulf. I am not sure what the CSA could do with it that Mobile would not suffice.