"Cleaning" Cleaning Off A Coin - Would This Work?

Professional coin graders would still be able to tell, most likely.

The damage done from harsh cleaning is eternal. There is no way to fix it. Even if you did pocket piece one for a year and played with it constantly the smoothing effect would only occur on the high points. Just like normal circulation.

Those protected areas found in the tight spaces of the design elements would still show cleaning, probably halos, and still be detectable.

If you can get down to P-01 you'd be golden. The only problem with that is that everyone you met for the next five years would think you were a bit strange because you were constantly playing with something.

I'll tell you, my cat wasn't happy about it.

Imagine taking a show type car with a mirror finish and using a wire wheel to make it not so nice. Then entering it in a car show.

Andrew is correct. First it depends on the amount of cleaning. I've noticed that many collectors call a coin with many hairlines Harshly Cleaned." Of course this is nuts.
A normal amount of light cleaning can be removed as a pocket piece but the grade should drop less than a point UNLESS it was on the line to begin with. Many old time dealers carried a pocket full of stuff around in their pockets. Even a polished coin can be brought back to an acceptable condition - but who has the time to wear out some pockets these days.

I think if I worked a a paint store I would have a jar of "media" around to work on coins while shaking paint.

I tend to agree. Event if it is something that really gouged the surface, this could be true if being worn smooth and thin is what is needed to remove all traces of the harshest cleaning.