What is more likely to happen, especially with modern arrows, is for an arrow to damage the nock of another arrow and then keep going. Or the arrow might strike another arrow on the shaft, possibly denting or breaking the shaft.
Or, like in the photo below, it might hit the nock and drive in far enough that it stays there.
In order to actually split an arrow lengthways - down the whole shaft - it would need to be following:
#1. The arrow would need to be made of wood.
#2. The arrowhead would need to be razor sharp (typically made for hunting).
#3. The shot would have to go not only at the right spot, but also drive inwards at the right angle. A degree or two up or down and the arrow which just damage the arrow it is hitting without driving its way down the shaft.