No, it won't. There's a big random element to this, especially when you are prompting GPT-4 directly through the ChatGPT interface.

Image generation models can sometimes produce the exact same image if you fix the seed they are using - there are different procedures for doing that for different image models.

LLMs like GPT-4 can have their "temperature" dialled down, but even at 0 they aren't guaranteed to return exactly the same response to a given prompt. I believe this is because they run floating point operations in parallel across multiple GPUs and floating point arithmetic isn't actually commutative - you can get back a slightly different result if the multiplications run in a different order.