Welcome, TDID. I'm guessing that your question reflects that you really liked Cicci as a character. Most people here do. Using Joe Spinell as Cicci was one of FFC's casting triumphs. He's got a small role and very few lines, but he's so absolutely perfect that everyone remembers him.

I think Cicci did "move up" somewhat during the film. When we first see him, he's in the background when Michael and Sonny are saying goodbye, then around the piano during the Mob war, then crowd control when Sonny beats up Carlo. But by the end of the film, he seems to have gained some importance when he tells Tom and Tessio that "the boss says for you to go on ahead..." And, as we saw in II, he's Pentangeli's right-hand man.