Can I bake pita bread on a pan?
The answer is almost certainly yes.

The almost is because I haven't made pita bread this way - but I have seen chapati made on a skillet, and under the right conditions it will puff up, even into one big pocket - so pan cooking doesn't specifically preclude that kind of development.  Beyond the need for it to puff up into the pocket, I don't imagine pan-cooking pita bread is that much different form other kinds of pan-cooked flat-breads.

it looks like cast iron is preferred, since it can be heated very hot and has the thermal mass to hold the heat steady while the pitas are cooking - but I honestly expect you can make them with any skillet you have on hand.
Stove-top pitas may be a touch drier, slightly less puffy, but have more browning (and toasty-flavor) than oven-baked pitas, because they're in direct contact with the heat, instead of being cooked by radiant heat.  You can press the surface gently with a clean towel to help the pocket form if it isn't forming quickly or fully enough for your tastes.