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 Allison Murray died in 1959.
Nathaniel Alexander - bishop - died in 1840.
Nathaniel Fillmore died on 1863-03-28.
Nathaniel Gottfried Leske died in 1786.
*SPOILER ALERT* *SPOILER ALERT* *SPOILER ALERT* SCROLL DOWN He sacrifices himself to save Bart and kill Nouda
Oh, dude, spoiler alert! Yeah, Nathaniel totally bites the dust in "Ptolemy's Gate." Like, he sacrifices himself to save Kitty and Bartimaeus. It's a real tear-jerker, man. But hey, that's the price you pay for dabbling in magic and power, am I right?
Nathaniel Wanley died in 1680.
Nathaniel Cotton died in 1788.
Nathaniel Chapman died in 1853.
Nathaniel Bowen died in 1839.
Nathaniel Dearborn died in 1852.
Nathaniel Hitch died in 1938.
Nathaniel Gould died in 1919.
Nathaniel Grubb died in 1760.
Nathaniel Appleton died in 1784.
Nathaniel Brent died in 1652.