I wouldn't put 100% stock in the immigration date, because memories fade and he may not have been the one to give the information anyway. My husband has ancestors who gave a different year of immigration for every census.
Also, people did immigrate young in those days, so I don't think 15 wouldn't have been out of the question.
Hopefully, we can rule in or out this Patrick one way or another.
Do the Army records that said Patrick went to the US have any further detail?