There is no James Gillen listed in the index volume of the Naval Official Records. However, there are two other similar names, which, because of the numerous errors in transcription, may in fact be the same person - your James Gillen.
One is listed as James Gilland, who served as seaman on the CSS VIRGINIA, 1862, and the other is James Gilliam, listed as a seaman on the CSS CHICORA, 1863-64. I would suggest, that if you proceed with further research, you may have to look under these variants of his surname, as well.
In my research of the personnel of the CS Navy, I have sometimes found two or more variants of a surname, but they are usually the same person. An example is a sailor named J.J. Lugenbuhl, whose surname is also shown as Logenbuhl, and even as Sugenbuhl, all obviously one and the same person. His proper name, as shown in his pension papers, available at the Louisiana State Archives, was John Julius Lugenbuhl. I am slowly compiling a comprehensive roster of the personnel of the CSN and the CSMC, and trying to cross reference different variants of some names shown, and, if I come across evidence that two or more surnames are of the same sailor or marine, then I note that down in my CSN roster.