Yes, the Car-Net ID is the "commission number" of your vehicle which is also listed as such on your Monroney sticker. Commission numbers, as a production control element, precede VIN assignment at the factory. Typically when ordering a vehicle receiving the commission number signifies that a build date has been assigned (we didn't get that for initial ID.4 orders as part of the "status wheel" but perhaps now available?).
btw: The EA assignment number has to be provided by them via your salesperson upon delivery. My salesman called to get mine while I was with the finance guy.