I thought the main factor of the fall of New Orleans was the fact the bulk of it's garrison was sent north to fight at Shiloh when the Union attacked.
It is significant that the city surrendered to the Union fleet, not the Union Army. This speaks volumes about the vulnerability of the city to attack from the river.
If the full garrison had been there, the city might have tried to withstand a siege, but I doubt it.
--There was nothing at New Orleans itself preventing the Union fleet from flattening the town via bombardment if it didn't surrender...the city depended on the defenses at forts Jackson and St. Philip to stop an enemy fleet from getting there in the first place.
--If the Union fleet bombards the city and destroys it, the city is rendered useless to the Confederacy, so why bother trying to defend it?
So if the Union fleet gets through the Mississippi River defenses to the city, the city will fall, regardless of whether the full garrison is there or not.