Will parchment paper produce dramatically different results?

There's always the old standby of foil.

The oven temp is above the burning point for paper (which is 451 F), so I wouldn't recommend it. In practice, your parchment probably won't burn all over but you may get a lot of charring and crumbling around the edges and where the paper isn't covered by potatoes, leaving you with lots of burned paper bits to get stuck to the potatoes.

I would instead just lightly oil your plain metal pan. The potatoes will be well oiled and the high heat will sear them, so as long as you wait until that searing happens to flip them, they won't stick.

Parchment paper should be fine. Results should be the same