I would keep a fairly close eye on this. Although there may not be anything harmful in the cardboard, it could cause a blockage in the digestive system if too much is ingested.
Just keep an eye on how much he is actually eating and how much is just being ripped off... if he's anything like my bun, I'm sure you'll find little mountains of ripped up cardboard around the place :roll::lol:
As usual, just ensure that he eats plenty of hay. This is high in fibre, so will help 'push' food (and anything else) through his system