Since all we know for sure about our James Sweeney (my great granduncle) son of Patrick Swiney and Margaret Hayes/Keys, is that he was born on 25 Jul 1870 I've decided to do a bit more digging.
I'm also wondering whether perhaps the James Sweeney at 1519 Ferdinand was perhaps a more distant relative ? Not his mother's brother, but possibly a cousin of his mother (Bridget Sweeney b1869) ? Maybe a bit more digging will turn up another younger James.
Regarding our James Sweeney (my great granduncle) I found that in 1901, age 32, he was at 33 Mulberry Lane Mitchelstown Co Cork with his parents and 3 younger siblings. But I can't find him in the 1911 census. So it's possible that he did go to America, but so far no luck finding him.
I've really not touched the Sweeney side of the family as far as research goes, and the surname Mulroy isn't familiar at all.
Edited to add: I've just found that our James (my great granduncle) was in Ireland in 1906, informant for his father's death registration.