Yes. One thing Coppola wanted to do (per his Notebook) was have Michael "emerge" as the don. You see little glimpses in various meetings, and it's finally full-blown when he visits Carlo.

I can't think of where I heard it, but I think Coppola talked about "succession" being a continuing theme of the first movie? It certainly is in the novel: very early, Vito thinks that Sonny wouldn't be a suitable successor as don. In the course of the war, the aging and mellowing of Clemenza and Tessio become a factor.