To each their own and I wouldn't judge another parent for this but personally I don't believe in humiliation parenting. I had some experience with it growing up though so I may be a little oversensitive to it.
Depends on what he did, and in this case HOW he was bullying. If it was extreme and he simply didn't see anything wrong with what he did, then yes. There would be punishment either way, for me to implement this punishment it would have to be extreme, or he just simply did not think/ care that he was in the wrong. My mom always told me if I ever stepped out of line, she would come to school to pick me up wearing her underware on the outside of her pants, and make sure she smeared chocolate jello on them first...then introduce herself to everyone as my mom....just the threat itself was enough to make me behave for years lol.