Yes, and note that Barzini and his group arrived late, and seated themselves far from the dance floor so that Vito would have to go out of his way to greet them. Brando seemed as enthusiastic as Conti about that meeting, which makes me wonder why Barzini was able to trick Vito into thinking it was Tatttaglia and not him all along.

Interesting (to me) also is that Clemenza went out of his way to say he "hates that God damned Barzini."
No capo ever said he hated the Tattaglias...and when they were discussing the killing of Phillip Tattaglia it was as much a comment on Sonny's temper as it was on the death of an enemy.