Does the Apple Pencil work with a screen protector?

Yes, according to the Apple support forums, MacRumor forums and other various user comments lots of iPad Pro owners use their Apple Pencil with a screen protector. Even the Zagg InvisibleShield comments and questions section mentions that the Apple Pencil works well with the popular screen protector.

You can also use the Apple Pencil to trace through standard paper, like a piece on computer paper.