Can you use a threadless headset on threaded forks?

With a threaded headset the steerer tube ends just above the top tube, and the protruding end is threaded. The top headset cup screws down over the steerer tube and presses a set of ball bearings against another cup that's pressed into the top end of the head tube. Then the stem, the part that holds the handlebar, is L-shaped, and one end fits into the steerer tube.

With a threadless headset the steerer tube continues up a bit, the stem is basically a straight part that fits over the steerer tube. The top cup of the headset slides down against the other bearing parts and is forced downwards by the stem and a compression cap.