I think that's a complicated question.

But, in the end, I think the answer is "yes."

Not so much because he wanted to be Don in and of itself but because he wanted certain things out of life (power, success, the ability to make his own choices, legitimization of the Corleone name) and he realized that he could best accomplish them by becoming Don.

I always think back to the scene outside the hospital when Enzo's hands are shaking. Michael lights his cigarette for him and looks down to see how steady his own hands are. I think, right then, the lightbulb goes off in Michael's head - "I'm good at this!"