No. They both likely knew what Greek Fire, in the literal and classical sense was in general (i.e. a firey sulphuric compound that was flung in boiling pots and the sort from catapults onto enemy ships). Mann, seeking to convey a discription of the way the yankees were shelling Charleston with live explosive shot, used the term figuratively to the pope. It would be the same as the U.S. today telling somebody "we bombed the crap out of the Hussein regime." Does that mean we literally caused Saddam to soil himself? Or perhaps that we dumped large volumes of manure over the skies of Bagdhad? Not at all. It is a figurative statement that accurately describes the extensive nature of our air campaign during the war.
That is possible, I suppose. I have no idea if he had any military background at all.
As I noted previously, at age 70 in 1863 he would have been old enough to have lived through the napoleonic wars that consumed practically all of Europe. It is therefore WITHOUT A DOUBT that the pope knew of warfare's progression well beyond the days of medieval seiges.