Yes and no. You might get the same output if you turn down the temperature, but you will probably not know the output without running it first. It's a bit like a hashing function. If I give the same input I get the same hash but I don't know which input will to which hash without running the function.

Also most LLMs are not run as I write a prompt and I will read output. Usually you have MCPs or other tools connected. These will change the input and it will probably lead to different outputs. Otherwise it wouldn't be a problem at all.