I recall seeing signed paddles in high school. As often as I was paddled, I was never asked to sign one. That must have been just for the BMOC? The principal broke a lot of paddles, so any signatures were temporary. He always brought two to a paddling session for insurance. He stuffed them under his belt, buttoned his coat and he was good to go.
I recently saw a picture on a spanking blog of a paddle with signatures and it made me wish I had asked some of the little darlings who have felt my paddle over the years to have signed it. It would have been a nice memento.