I don’t know. Agnew’s father was an immigrant, but I don’t know when (or if) he became a naturalized citizen. Was his mother also an immigrant?
According to census records, his immigrant father was a resident alien (non-citizen) and his mother was American when Agnew was born. I don't know if he received citizenship later but the important fact is that he was not a citizen at Agnew's birth.
According to a poster, MGB, here: http://www.therightsideoflife.com/2010/02/22/eligibility-hi-petition-launched-in-spite-of-introduced-bills/ they state that the 1910 and 1930 Census, as well as Agnew's father's WWI registration card state the he was a Naturalized citizen. His WWI reg card is dated Sept. 12, 1918 and Agnew was born Nov. 9, 1918. Coupled with a 1910 census listing that status, it appears that his father was Naturalized prior to the birth of Agnew. Therefore, Agnew would be NBC.
Of note, apparently the 1920 census lists his father's status as alien. However, that same census also lists the wrong year of his immigration.