CCS1, the physical connector used in North America, yes. CCS the wire protocol, no. NACS is a physical Tesla connector using the CCS protocol.
The CCS adapter used here not working basically tells you the Cybertruck doesn't want to talk CCS yet. A CCS charger with a Tesla adapter is essentially equivalent to what NACS will be. This also means that as it currently stands the Cybertruck won't be able to charge on non-Tesla NACS chargers without an update.
On Superchargers this is not relevant. Superchargers can talk Tesla's own protocol (which is not in NACS, and is CAN-based) to the Cybertruck and can talk the NACS/CCS protocol (PowerLAN) to NACS cars / CCS cars with an adapter.
