I would like to make a cheesecake with confectioner's sugar and though it's been awhile since I've made cheesecake, I believe I used normal sugar before. However, I only have confectioner's sugar on hand at the moment.
I have done this, and it was regrettable. The flavor of the cheesecake was acceptable (not great though), but the texture left something to be desired.
Like Dorothy pointed out, there is cornstarch in confectioner's sugar. This left the cheesecake I ended up with incredibly dense, and it also cracked (more than usual) while baking.
I would not recommend using confectioner's sugar as a substitute for granulated sugar when baking a cheesecake based on my experience. I certainly would not try it again. At least, not without taking the time to do something to offset the cornstarch effect. Adding a liquid could do the trick, but right now I would be guessing on what and how much to use.
It's easier to just head to the market for what you need in this case.
While you could use it, it would likely affect the finished product. As a substitute in baking, when the recipe calls for granulated sugar, powdered sugar is not always suitable. And, although it is granulated sugar which has been processed into powder, cornstarch has also been added to prevent clumping.
With sugar, the size of a granule determines how well air incorporates into the batter. The larger the granule, the more air and, since the batter needs that air to help it rise, using powdered sugar will not produce the same results.