IIRC, during the '76 campaign Carter used W. Averell Harriman as a back channel to the Soviets. I'd have to dig through my notes to find my references on that, but I believe it's discussed briefly in Rudy Abramson's Harriman biography.
I got a chance to look just now, and Abramson does discuss Harriman performing that function for Carter on pp. 688-691. There's another recent book on Carter that discusses this, but I don't recall the title offhand. I don't know if Carter used Tunney this way. Kennedy would've been aware Tunney was talking to the Soviets, but I don't know if he knew he was working for them. Kennedy and Tunney may well have been arrogant enough to think they were clever enough to play this game and use the Soviets instead of being used by them--I would not be surprised if they don't see themselves as traitors because in their eyes they're "above the law" that binds non-Kennedys.