CGNAT does not means unroutable IP, it just means you would only have assigned a small range of ports on a routable IP with others.

If you have CGNAT, the IP on your router's external interface is unroutable.

Just like how when you do NAT for your home network, your devices get assigned non-routable private use only address space.

Unroutable meaning not publicly routable. Of course you can route traffic through your own LAN to your Internet gateway.