Italian citizen, but born abroad

My GGF (-GF-F-Me) was born in Argentina but moved to Italy in the early 1900s. His parents had moved to Argentina for 4 years, had him, and then moved back to Italy. My GGF became an Italian citizen, served in WWI, got married to an Italian woman and then moved to the US. He later had my GF and then naturalized as a citizen in the mid 1930s.

Can my GGF qualify as my most recent Italian ancestor, even though he was not born in Italy?