My experience (I just tried this on my Model 3) is that if the car is in deep sleep, pushing the button on the cable won't do anything at all. If it's working for you, then likely the car is not in its most deepest sleep state. I'm in the habit of slightly depressing the rear door handle to wake the car. At that point, if I have my phone, I can remove the cable with the button press.
FWIW I'm on the latest firmware and have HW3. The behavior has been the same (inconsistent dependent on sleep state, not firmware version) since I've owned the car in early 2018.