I think the answer is that they can be added. As nbr1 suggest I think that in rock vertical loads are inmediately diverted through interlock (shear at the interface, more than friction, really); i.e., the axial stiffness path is shorter with a number of inclined struts to the sides of the pile that to the bottom of the same. Then if the interlock fails we have some kind of friction and I see then secondarily axial stiffness to the bottom developing. Nut I think can be addes at least for a final strength if what you are considering is really skin friction and not shearing the rock (or concrete) at the interface, for some level of friction will be developing as soon as the interlock breaks and load is starting to be transferred to the bottom, and to make fail the pile you will have in the end both tip resistance and side friction.
For service level loads, the ideal situation would be values that do not break the interlock a situation where you (for homogeneous rock) would be more or less compressing an elastic rock. To make use of the full process, some characterization by test would be very convenient, you will have somewhere to read appled loads and settlements atop the tip till considered failed.