In the Bot Framework, a the MessageType.ConversationUpdate is described as follows:
This notification is sent when the conversation's properties change, for example the topic name, or when user joins or leaves the group.
When a bot is connected to the Facebook channel, do they receive a ConversationUpdate message (or any other system message) when a user deletes their copy of the conversation in Messenger, or does the deletion only occur on the user's end without any notification to the bot?
No notification is sent when a person deletes a conversation. But even if they delete the conversation, you can still send messages to them inside the 24hour standard messaging window.