@j2kun I don't know if this is a helpful answer, but honestly: It depends on the controller.
Firstly, there are two completely different ways of implementing PID, one kind of looks backwards and one kind of looks forwards, and they give very different results.
That's not even getting into the details of the implementations, the quirks of each system.
So I know I'm ducking your question in a way, but it really does come down to, your system probably operates in a way completely different from so many other systems, so there is no standard answer to a question like this.