It is uncertain whether or not he did die, and in fact his absence suggests that he might have. However, it is mentioned in one of the earlier books, Amulet of Samarkand I think, that sometimes a spirit who has been imprisoned for a long period will grant a favor or favors to the individual that freed him. Under this rule, there is a possibility that the two that were in the staff may have protected or spared Nathaniel in gratitude. But then again, they could've been some of the more ill-spirited types and could've killed him. Up to the reader to decide I suppose.
Nathaniel Spence died in 1914.
Nathaniel Fillmore died on 1863-03-28.
Nathaniel Gottfried Leske died in 1786.
Nathaniel Allison Murray died in 1959.
Nathaniel Alexander - bishop - died in 1840.
*SPOILER ALERT* *SPOILER ALERT* *SPOILER ALERT* SCROLL DOWN He sacrifices himself to save Bart and kill Nouda
Nathaniel Hodges died in 1688.
Nathaniel Peabody died in 1823.
Nathaniel Heckford died in 1871.
Nathaniel Jocelyn died in 1881.
Nathaniel Woodhull died in 1776.
Nathaniel Garrow died in 1841.
Nathaniel Littlefield died in 1882.
Nathaniel Sylvester died in 1680.
Nathaniel Ireson died in 1769.
Nathaniel Morton died in 1685.
Nathaniel Spinckes died in 1727.