The technical answer is yes, the lens can be attached to the camera and you can take photos. But it is a compromise in so many ways.
The easy rule of thumb with FX and DX formats (Full frame compared to APS-C frame) is that the lenses are the same mount. But they project a different size image on the sensor. FX lens will project the large image for a full-frame sensor. It will also project that same image onto a crop-sensor (DX). The result is a smaller portion of the image is recorded on the sensor. This works fine and sometimes gets better performance from a lens because the photo is recorded by only using the best part of the glass in the center. But attempting the reverse with a DX lens on a full-frame sensor means that the camera must do a digital crop and only use the center part of the sensor to record the photo. The image below I borrowed online shows this relationship.
Added into this equation is your camera viewfinder. That view won't change, you still see the full-frame size image there, with an illuminated rectangle frame that represents what the image recorded will be. At least my D750 works this way, I expect your D4S to be the same as it is a contemporary of the D750.
So the DX lens on your D4S is going to result in a smaller size photo, a cropped-in size, and much lower resolution. I cannot recommend doing this. I have done the experiments already.
Further let's examine your goal with the 12-24mm lens, the expected results, and why it might be a waste. DX cameras are not the right tool for ultra-wide work. Kind of why there are so few ulta-wide angle lenses for DX format. The Tokina lens is 12mm-24mm zoom range, which translates to 18mm-36mm full-frame field of view with the cropping of the image. Your typical 24-70mm full-frame lens is going to cover half of this range as it is with full resolution. You can buy a manual focus 14mm prime lens to take the ultra-wide photos and it would not cost too much at all. There are also autofocus 14mm primes for some more cost if it is required. At the ultra-wide end, that autofocus is not as much of a benefit.
That is my assessment. I do this for benefit of future readers seeking an answer with a similar camera-lens combination.