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Pretty much. It seems to have been an Irish regiment raised by James II in France in the 1690s after his exile, organised and equipped as a regular French cavalry regiment, and was shipped over to Scotland in 1745 to support the rebellion. There's some more info about the regiment here: http://www.kronoskaf.com/syw/index.php?title=Fitz-James_Cavalerie
I just looked up and it seems like the colonel was one Charles de FitzJames, James II's grandson through an illegitimate son (hence the surname FitzJames), from whom the Duchess of Alba was also descended, making Charles her great x 7 uncle or something like that.