Hey @Deon Don Racheal from the support engineer team here 

It is not possible to trigger a workflow from the composer, although I love this idea. I’d be happy to flag this as a feature request for the team to consider!

Far from ideal, but could you have the agent set a people attribute that would then trigger an outbound bot?  you would basically have to tell them that you would trigger the bot in another window and have them close your message and open the other one?