I have been playing with my wife, and you can already join convos and vote. By joining I mean look at the cutscene and listen. Voting doesn't do anything though. It just shows which option you want. I doubt they would let other people interject in a conversation at any point. That sounds like a nightmare to script. Especially in 4 player coop.
I don't mind waiting though. It kind of reminds me of playing TTRPG's. You wait and listen while another player is playing out a scene with an NPC.
