Fiber Optics as a video source and a switch?
Yes, assuming you could keep the grid organized so that you knew the order/position of each fibre.

Additionally, in order to recognize touch, you'll probably want to look at reflected light on a per-fibre basis, which will require non-trivial optics and electronics. Alternatively, you could embed capacitive sensors in the "end" of the cable, but this ruins the optical isolation and its associated advantages.

You should really consider if it's possible to use a simple LCD w/ touchscreen.