I haven't looked at the network activity itself, but at the very least, having cloud messaging turned on is allowing the connection to Google to happen. Usually, the UI prevents having registration off and cloud messaging on, but apparently only the UI prevents this, and it's not prevented on the backend. So, cloud messaging can technically function in some form with the registration toggle off - not without some serious problems, though, as @cde pointed out in earlier comments.
@mar-v-in
Quote:
See here: https://gitlab.com/CalyxOS/calyxos/-/issues/2674