Sync limitations
Intercom doesn’t consider outbound messages without replies as conversations.
We found that if an end-user doesn’t reply to outbound messages (such as emails, posts, or chats), we can’t fetch the conversation IDs because the REST API does not return them. As a result, we can’t sync these conversations to your destination.
I want to see who gets which outbound. When can we get ability to get this data programmatically? @Azure Radio 277
That is true, they are not conversations (yet). But there is still a Message, and you can list them and read them through API, they have their IDs.
Messages without Conversation ID in the JSON are basically outbound messages that end-user did not reply to (yet).
At least this is my understanding of Intercom API docs, I'm not a developer, I just try to understand it 
https://developers.intercom.com/intercom-api-reference/reference/messages-model/p>
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