[mickael]

The notification are for signaling. The message notification can be distinct and encrypted using standard push notifications. If the problem is with metadata around the conversation (like typing indication, etc), they still can be encrypted on the server but with a cleartext flag associated with them to tell if the content should be pushed or not.

[Andrew_nenakhov]

You do not want any kind of cleartext alerts on read receipts or typing notifications. Most people also don't want apple to know what type of data is transmitted to your app.