In a rigorously fascist regime, the relationship between the leader and the nation is viewed to be organic, so elections are unnecessary. But the model for American fascism is more the Confederacy than the Third Reich, so the issue is more complicated than you might initially think. Would there be elections in fascist America?
In red states, yes. With the religious tests and censorship in place, there would be room for some political debate.
In the blue states, no. Even with the tests, censorship, and the occupying army, the population would be viewed as being too unreliable for elections. Reverse Reconstruction would take decades.