The irony is, though, even had Tessio and Barzini succeeded, Tessio's days surely would have been numbered. If Tessio was proven to be disloyal to the Corleones, how could Barzini have expected any loyalty at all from Tessio either? Someone as shrewd as Barzini would see Tessio's behavior as a deep character flaw, one that may be temporarily quelled but eventually would manifest again under certain circumstances.
In all likelihood, once The Corleones and all internal threats from within the family had been extinguished, Barzini would have had Tessio eliminated as well, replacing him with a figurehead whose loyalty had been proven and unquestioned.