Usually rabbits will just rip them up and maybe ingest small bits each day. The problem encountered when too much cardboard is consumed, is that it doesn't break down in the digestive system, and can form a gooey mass that can become an obstruction that leads to a GI blockage. I have read of personal accounts from other rabbit owners, where their rabbit has developed a blockage and gone into GI stasis due to excessive amounts of cardboard being ingested. It can even be fatal.
So it is certainly a concern. In most cases rabbits will just play with the tp tubes and not really chew and eat much of it. But if you feel like a lot of it is being eaten in a small amount of time, it may be better to use chew toys that are safer for your bun to chew, like willow toys, apple sticks, hard(dried) pine cones, and other rabbit safe wood.