Can you cook cut potatoes in a nonstick frying pan without oil?
That would depend on the cut of the potatoes, the heat and whether or not you put a lid on your frying pan.


If big cuts without a lid: They'll still be raw
If cut into small dice, heat not too high, with a lid on, you'd basically steam the potatoes in their own moisture and that would work.
if cut into small dice, high heat, no lid, you'll end up with charcoal on the outside and raw on the inside.


So yes, it's possible, but it's going to be finicky so if you don't want to use fat, what's wrong with:


boiling them 
parboiling them and then putting them for a short while in a convection oven?