Pretty sure Anthropic and other providers prepend these "official" system prompts to your conversation even if you send in a custom system prompt otherwise it would be trivial to produce CSAM, etc.
CSAM, and other harms, are typically detected using a set of specially trained, faster and cheaper models (and out of band matching techniques) that run before and after the main model.
Any mention in the system prompt is mostly defense in depth, and to make refusals more graceful.
Also, the system prompt, or even something reinforced on every message, is nowhere near as strong as its internal training or as an external safeguard.
If the prompt were the only protection, it would be extremely easy to produce illegal content after a long session.
I don’t think so. If you start a new Claude Code session without a system prompt, it doesn’t even know what model it is and hallucinates being some old variant of Sonnet.