Yes, Mr. Perfect Percy does this, although lately he seems to prefer the paper towels and any mail that we may have left on the table.
We must confess though, we kind of encourage his "shredding".
We get a ton of junk mail and he knows when I go get the mail we are going to play the shredder game. I stand back and toss him those annoying credit card offers and he proceeds to rip them to shreds.
One day, I left my paycheck on the desk in my home office...
(go ahead...finish the rest of the story yourself!)