It seems likely on the surface, but there are two or three potential problems I uncovered.
First, here is my line:
Great-great-grandfather Bartolomeo was born in the 1850s or 60s in Cuneo or Asti, Piedmont, and immigrated to the US in 1905 with his family, including Great-Grandpa John. Baccio never naturalized to the best of my knowledge, and he sadly died sometime before 1917.
Great-grandfather John Sr. was born in 1900 in Cuneo or Asti, Piedmont - probably in Costigliole d'Asti - and immigrated to the US with his family in 1905. He never naturalized, either - even after fighting for the US in both World Wars. John Sr. did file his first papers, but never went further. He is listed as an alien on every census until 1930, when he was listed as first papers. But in the 1940 census, he is again listed as an alien. He married Great-Grandma Isabel, a Portuguese-American, in 1928.
Grandpa John was born in 1928 in California. His parents were married at the time, but Isabel had the marriage annulled in 1933 or '34. This was after Grandpa John was born. Grandpa John was then legally adopted by Isabel's next husband.
Mom was born in California in 1956. She never married my father.
I was born in California in 1994. My parents did not marry, but both are on my birth certificate and I've met them both. I do not get along with my father, and I don't know if he would be willing to issue an official statement of paternity if I tried to contact him.
Nobody ever seems to have renounced their Italian citizenship.
The problems, besides my not having all the documents, are that I was born out-of-wedlock, John Sr.'s marriage was annulled, and my grandpa was legally adopted by Isabel's next husband. Will these bar me from becoming an Italian citizen? My mother would also like to apply at some point.