You can click the other person while they're talking to see what all is said ont heir end and the NPC's. It's so that the other person can CHOOSE not to be drawn into other conversations, notably so that if one person is trying to do the competitive coop thing and sneak some quests in, y'know... And also because sometimes you want to talk to an NPC on one player and your friend robs said NPC blind.

But yes, if PLAYER ONE is talking to TIMBILLJOETHENPC they will have an obvious little thing above both character's icons. If you click either character, PLAYER TWO can see the dialogue.