I think that the Corleones under Sonny would have fought to gain justice or vengeance over Vito's killing. I think that Sollozzo and the Tattaglias would have fought because they had committed to get the drugs project started (which they couldn't do in wartime), and also because the Corleones were attacking them. (The surprise in the war would be if Barzini threw his men into the fight against the Corleones).

I should say that by "all-out war" I meant between the Corleones and Sollozzo/Tattaglia (and maybe Barzini) at this point. I think the refusal of the Corleones to give up McCluskey's killer is the incident that sets off the war against all of the other families.