The DIC is in the original radio. If you remove the DIC, a bypass module has to be installed as part of the retrofit of an aftermarket radio.
If you don't have that bypass module, then an essential part of the car's computer system is missing and no, it won't start.
The CTS isn't your grandfather's Caddy. Nearly all the electronics in it are networked into the car's own LAN and any changes made to it have to be acceptable
to the ECU. Removing the DIC and not putting a bypass unit in place is not acceptable to the ECU.