To use this as a sales platform. I think it would be important to hide the conversations between the operators. Only the admin should be able to see. If the sales consultants could see the other conversations they could use their leads.
If the operator is not available to take the chat then the chat would be made available to another operator and only then would the conversation be shown to the new agent/operator.
I think this would be popular feature because its how most chat platforms already work.