My guess is that Tessio would have joined Luca Brasi and slept with the fishes. I don't imagine Barzini was going to sit by and watch Tessio -- who had already betrayed Michael -- accumulate any power at all so that he could turn on him.

I doubt Tessio would have assassinated Clemenza. Pete struck me as the type of guy who would be loyal to whomever kept him alive. I'm sure he'd have cast his lot with Tessio and been quite happy.

Barzini was just trying to solidify his power by making the move with Tessio. Don or no don, Tessio would be beholden to Barzini for having engineered the whole thing to begin with.