No, it does not specify a grade of glass paper as such. In fact, there is a rough cylinder included that could be used to reduce the nail more dramatically, but the polish heads are more like a smooth, leather texture that, when rotated quickly, bring out a polish. I see this as being the main use; ie. the last stages of polishing. However, with a minimal amount of effort, I suppose glass paper of your choice could be wrapped around the fast rotating cylinder.
This brought back memories of working with plastics in design technology at school. I remember polishing the edges of a piece of plastic that had been cut with a hacksaw. The polishing tool was also rotating cylinder that we pressed the rough edge of the plastic on to for a smooth finish. Exactly the same principle at work with this device.
D'Ammassa Spruce/Spruce Double Top