'Converse' is a combination of 'verse', which means 'words', and con-, which means 'with'. To converse is to talk with somebody. A conversation needs a second person in order to be a conversation.
We as humans need to talk. Conversations help us think our thoughts, solve our problems, relive our glories, dissipate our failures. That second person can provide ideas and insights that we may never have come up with on our own.
Sometimes, though, the second person doesn't need to provide anything. Sometimes they just need to be there and listen. Being a sounding board can be just as beneficial, especially when a person needs to sort out their thoughts more than solve a particular problem.
In writing, a sounding board character is tricky. If we only see one person talking, it seems like a monologue. Then the listener ends up being like the little six-year-old girl. However, a visual cue here and there may provide enough input to express that two people are there, but one person is doing the talking for both sides.
You could make for an interesting scene. Give it a shot.