The NC/GA gunmaker named James A. Gillespie was born in 1822 so he would have been only 14 years old when the Alamo battle was fought.
However John Gillespie the NC gunmaker had two brothers that moved from the Cowpasture out to the Holston River area of VA just before the Rev War. One of the brothers was named James and he died in 1834 before the Alamo battle.
I have not researched this line of the gun maker family but I do know that many descendants of these two brothers moved to TN. Also Old man John Gillespie the NC gunmaker had a brother named James that lived in the Greenbriar area of WVa and I have heard that some of his descendants moved to TN. Also there was some inter-marriage between the Crockett's and the VA Cowpasture Gillespie descendants. Also I understand there was a Gillespie forge/gunshop in the same county where Crockett lived, forget the county name, maybe Greene??)
So its very likely that the James Gillespie that you mentioned was a descendant of the Gillespie gun makers.
Dennis