Parchment paper around a cheesecake?
With a properly non-stick springform pan, the cake should shrink and pull slightly away from the edges as it cools. Don't do anything to it until it's fully cooled (to refrigerator temperature). At that point a spatula might help release, but probably wouldn't be necessary.

I would expect parchment paper to be counterproductive. It would absorb some liquid during cooking and become more adhesive than your non-stick pan. Also, it would make forming the crust against the sides trickier.