... it depends. In many cases, such as high-rise office buildings, the elevator shaft walls are designed as part of the building's shear walls. You may certainly use the enclosure of your elevator shafts (shaft is really a term best used for the actual hole, not the walls) to support structure above as long as you show them thick enough.

That's a great question!  And the answer is yes, as Non Sequitur notes.

To the terminology question: shaft, shaft enclosure, and hoist way are all involved here, often confusingly so.

fun fact, the connections should be detailed so that the beams may fail without harming the shear walls ( fire cut)

Yes, shaft walls can be load bearing. 

Generally speaking (there always will be exceptions) shorter wood buildings shaft walls are load bearing while taller concrete o steel buildings are not because structural columns do that work, however if needed they can be engineered to take some load. 

in tall structures elevator and stair shafts are usually used to control shear

Yes, also as a shear wall.