I think you are right. Any Latin American government with the military in control, that was supported by the Roman Catholic Church and a residual hispanic land owning class had important interests in common with the Spanish Nationalists. As a result of the damage the great depression did to democratic credibility in the region in the early 1930s, there were a large number of such Catholic/military/landowner regimes in Latin America that were inclined towards the Nationalists.
However, they mostly maintained de jure relations with the Spanish Republic until February-March 1939, as it was the legitimate government in law. Only about five opened de facto relations with the Nationalists before then.
The US leaned heavily on El Salvador, Guatemala and Nicaragua, to prevent them sending diplomatic representatives to the Nationalists after their recognitions in November 1936, and dissuaded any other circum-Caribbean countries from following their example.
In no cases were ideological Fascists in control of Latin American governments. Indeed, major countries such as Brasil, Chile and Argentina legislated against such organizations in the late 1930s after real or perceived coup threats from them.