It changes some behavior, but there's some things that are frustratingly difficult to override. The GPT-5 version of ChatGPT really likes to add a bunch of suggestions for next steps at the end of every message (e.g. "if you'd like, I can recommend distances where it would be better to walk to the car wash and ones where it would be better to drive, let me know what kind of car you have and how far you're comfortable walking") and really loves bringing up resolved topics repeatedly (e.g. if you followed up the car wash question with a gas station question, every message will talk about the car wash again, often confusing the topics). Custom instructions haven't been able to correct these so far for me.

For claude at least I have been getting more assumption clarification questions after adding some custom prompts. It is still making some assumptions but asking some questions makes me feel more in control of the progress.

In terms of the behavior, technically it doesn’t override, but instead think of it as a nudge. Both system prompt and your custom prompt participates in the attention process, so the output tokens get some influence from both. Not equally but to some varying degree and chance

It does. Just put it in the custom instructions section.

Not for me, at least with CharGPT. I am slowly moving to Gemini due to ChatGPT uptime issues. I will try it with Gemini too.

The system prompt is there if you use a chat app like ChatGTP. The system prompt is one of the things that controls the behavior of the app.

If you use an LLM endpoint in Azure OpenAI, no system prompt is in effect unless you provide one.