Your rat will love it. Mine drag theirs all over the cage and chew them to pieces. While they chew it, I don't think they actually eat much of the cardboard, i think they just gnaw on it. And I haven't read anything about it being bad for them.
Toilet paper rolls are one of my girlies favorites! They drag them, go through them, scammper over them, chew them, pee on them, play in them, sleep in them, and love them! That and any hting else chewable, and "rat home" worthy.
Our girls get a new toilet paper roll every few days and they love them. They shred them and use them for bedding... or just shred them for fun... or just carry them around. They have an odd habit of putting the shreds in their food dish, as if trying to hide the food. One of them likes to stash her wooden blocks in the food dish, too. Rats are weird.
I use the toilet paper rolls and the paper towel rolls and make a kind of maze with treats in them at different places and let them at it during free play. I also use the toilet paper rolls as pinatas for thier cage. Just fold in one end of the toilet paper roll, put some treats into it, then fold up the other end. You can cut small holes in it to help them out or leave it whole so it is a challenge. I sometimes hang the pinatas just high enough they have to stand up on thier hind legs to get to it. Keeps them busy all night long. It also keeps my daughter up all night long, so we only hang them on weekends..
I put 2 toliet roll tubes in for my 3 girls
and they seem to like them
there not very very intrested in them but will occasionaly run through/over one
also i made a lil bed at of a small carboard box stuffed it with a shredding baby grow and there normal fluffy beddin and regular shredded cloth stuff they seem to like that to ,
I also made a hammock out of a fleece babygrow but my girls dont seem intrested unless i put them in there , so lazy!! my girls are 8 weeks 4 days