What is the shell of a USB-C plug for?
Will USB-C plug work without chassis of the connector?
Yes, it will most likely work with short distances, on your desk, as long as at least one side still has chassis connected.   

Will it still comply to USB?
No, USB requires a chassis connector for numerous reasons.


For signal integrity, the chassis of the connector shields all signals of the cable from the outside world inside the cable. The cable has shielded foil around all conductors. Breaking this shield is not recommended.
USB 3 is very high speed with relative weak signals.
For physical integrity, the chassis provides all the latching features and strength the connector has. It also prevents misalignment of the connector.


If you want your socket to be flush you will have to use a metal enclosure with your custom socket. Or use any of the existing options that will extend trough the enclosure.


Shield is at approximately the same potential as GND, but it is not used as return path for power.

USB C pinout