In Puzo's and FFC's minds, Michael was clearly diabetic by the end of Part 2. Here's a link to an early draft of their screenplay. If you scroll all the way down to the bottom, just before the flashback scene (originally scripted for Brando, not James Caan) there is a clear mention of Connie giving Michael an insulin shot in front of an 18 year old Anthony (obviously, another scene that was never made).

The Godfather Part II Screenplay - Early Draft