Can a new plant grow from half a Succulent leaf?
After waiting for a while, I am finally able to answer this question myself:

A part of a Crassula leaf is still able to grow roots and new leaves, even if the part that attached the leaf to the mother plant is missing.

I have tried this out myself. I left the half-leaf depicted in the question on top of soil, watered it occasionally, just to keep the soil humid, but not wet. After roughly 5 weeks the leaf grew a first root from the calloused end. For the photo I have flipped the leaf around, to better show the first root.



In the following month, it grew more roots, and after about a month, the first new leaves started to appear. 




At this point there is little doubt that a full plant can grow from this, given the right treatment. It is not different any more from full leaves growing new plants.

Update (June 2018): The plant is now 2 inches tall, and doing well.