If one goes with a historically supportable timeline, using the 1853-56 war as the template, with a causus belli in November, 1861, the declarations of war and active operations began four months after the same in 1853 (Sinope); that means the US and UK have until March, 1862 to plan, mobilize, and deploy various forces ... so, the US troops in the Gulf and on the southeast Atlantic coast could have been, and presumably would have been, evacuated, for the most part, leaving what amounts to a corporal's guard on Ship Island, Fort Pickens, and Key West in the Gulf, and the same at Port Royal and Hatteras on the southeast coast. The larger USN screw steamers would head north to the Chesapeake, Delaware, etc, escorting the troop convoys, while the ocean-going sidewheelers prepared for duty as commerce raiders and the sailing warships and smaller steamers maintained the blockade as best as possible until the balloon goes up...Absolutely.
So, let's return to the Atlantic. One of most important question: would it be wise to mantain Union-held strongholds on Southern territory, or the best thing would be to evacuate them (and how fast it could be done?)
The most important, of course, is Port Royal. Florida until mid-1862 could be considered as lost cause. The Albemarle Sound are close enough to the Norfolk, to make at least some supply of Roanoke garrison possible (and, the waters of Albemarle Sound clearly aren't suitable for large RN units) - or, at least, evacuation possible. But what about Port Royal?
Given that, historically, DuPont had landed Sherman's 13,000 successfully at Port Royal in November, 1861, and Goldsborough was to land Burnside's 15,000 at Roanoke in February using two different transport forces (the Port Royal transports were largely ocean-going vessels, the Roanoke transport group mostly coasters), and there was a fairly constant flow of supply ships, dispatch vessels, and warships going on or off station by the winter of 1861-62, withdrawing the 3,000 or so troops in the Gulf and the 13,000 or so on the South Atlantic coasts would not be a significant challenge. One obvious move would be to use the troops thus evacuated, and/or some of Burnside's forces and those of Wool in the (historical) Department of Virginia to take Norfolk during the short of war period.
Obviously, if the British could manage the Tanga and Dardanelles evacuations under fire in 1914 and 1915, hardly seems impossible for the Americans to manage something similar in peacetime, essentially, 1862.