Integration between Salesforce Messaging and external Chatbot service

Hi, We’re using Salesforce Messaging with MIAW SDK, and chat sessions are routed using Omni-Channel External Routing. An external chatbot

 handles the conversation first, and may escalate to an agent later. 

Question: 

 Is it possible for agents or supervisors to 

view the live conversation (MessagingSession) while it’s still handled by the external chatbot — before it’s routed to an agent?

So far, I know:

• Transcripts are saved and viewable after the session ends.
• Messages are sent using the Messaging REST API, so they are stored in Salesforce.
• But I haven’t found a way to show the live conversation in real-time to agents or supervisors.

Has anyone done this before or found a good approach?

Thanks! 

I my use case I need to use external Chatbot service from SF Messaging feature, So has anyone implement this before, The 

External Routing is the proper way to do this? Or there're any approaches that fit my use case instead of External Routing?  

My Integration flow may looks like this?