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Enter Hannibal Lecter. For his excitement, he wants to take down the crime boss Michael Corleone. Could Hannibal's calculating demeanor infiltrate the mobs infrastructure and take out the Godfather?

No

Now this fight is random.

Quite possible, if we're assuming this is Hannibal before he is found out and captured. If there's no reason to be suspicious of him I'm sure he could contrive some way to get close.

If this is after his escape then it would certainly still be possible. We're assuming the original timeline for Corleone and his power so the net they could generate to located Hannibal even if it was known he was after Michael would be somewhat less than what I think would be necessary to stop him in time.