Doesn't matter if they are busy or not, impatience is impatience. Something it would be helpful to understand is the loss of control that is associated with struttering. When you fake stutter, or pseudostutter as it is known in the speech language pathology field, you can, at any moment, stop the "struggle". You are getting a feeling for how people react to stuttering but not a feeling for how the stuttering feels for the individual who is doing the stuttering. What makes stuttering the debilitating experience that it can be is not just the embarrassment and the reactions of others. It is that it is actually a struggle to talk. They are "fighting their words" so to speak. They also don't know when the stutter will end or what the outcome will be. Stuttering is like sliding on ice in your car. You feel that "oh shit" feeling and hope everything turns out ok; sometimes the car stops (the word comes out), sometimes you keep sliding (the word is still stuck), and sometimes you hit a tree (you physically cannot get the word out). For your acting to truly come off as authentic you need to understand that this is more than just superficial bumps in speech but a struggle to talk.