Without cover traffic, its not clear to me that this would prevent a correlation attack from an adversary with resources.
Signal could probably force TOR connectivity (forcing websockets for those connections), which would conceal the sender even more, but would not stop correlation attacks.
This also wasn't made to stop correlation attacks. This is a measure to reduce metadata being stored on the server. Messages stored on the server won't have a "from" label that can be read by the server.