From page 502, volume 2, DICTIONARY OF AMERICAN NAVAL FIGHTING SHIPS:
"CSS Baltic, an iron and cottonclad sidewheeler, was build in 1860 as a river tow boat, and belonged to the Southern Steamship Co. She was purchased by the State of Alabama, converted to an armored ram, and turned over to the Confederate States Navy in the middle of 1862. Her first commanding officer was Lt. J.D. Johnston, CSN."
I don't know if this answers your question, or not, but if the Southern Steamship Company was owned by Charles Morgan, then it has, I guess.