Very individual. Even with my voice drop and stubble, it's taken me a while to pass. I am finally mostly passing I think. But my facial hair is blonde/red, so I don't have that 'blue' chin look that screams guy.
The voice does begin to drop immediately though. The facial hair follows closely after. I think it depends also on how feminine your face looked before T as to how quickly you pass. Somebody who looks pretty androgynous just with a hair cut, will probably fall into the realm of regular passability very rapidly on T.
Really, the voice and facial hair start almost immediately. Within a month or so. If you go off T, I'm not sure if these effects lessen or not. I know they don't go away.