It'd work, but since the contact patch is smaller than that of a pencil eraser, it'd take a pretty darn long time. I suspect someone at Tidy Mouse is amused by the idea of the world's more trusting people scrubbing their monitors with a mouse-ball. Frankly, I am, too. Yes, it really is free. No, they won't spam you.
Optomechanical mouses get filthy.
There's no way around it. Mousemats like 3M's excellent Precise Mousing Surface or EverGlide's even better units can reduce the amount of crud-transfer, but not eliminate it. When this happens, the traditional course of action is to chip and swab and tweeze the muck off the rollers. Clearly, What The World Needs is a simple, automatic mouse cleaning system. Enter Tidy Mouse.