To betray your father's son is to betray yourself. Whether or not the plot fails in the end is irrelevant. You have pretty much signed your own death warrant, which was what Fredo did by working with Roth (anybody really believe that Roth intended to keep him on had Michael been assassinated?).

True though, the scene is very much tied in with, and a clever psychological setup for Fredo's imminent demise.

Apple