I have a melamine cage with a tube (not a fleece tube, just a tube, I have fleece chewers)... but ya, mine's attached to the hardware cloth (wire) of the door. I don't know why you couldn't attach one to the side of the cage...you'd just have to drill permanent holes where the bolts would go, get two LONG carriage bolts and just attach it like you would on any cage.
The reason I didn't attach mine to the wall of the cage is because I just know I would accidentally drill one of the holes a little too far in one direction and then I'd have to drill again...and as the carriage bolts aren't like thin bolts, I didn't want to have that big holes in the side of my cage. But, if it was going to be a permanent fixture, I don't see why it couldn't be done.
A thought of advice (and this may be common sense, but you never know)... if I was going to mount one to the melamine... I would put a washer between the outside of the tube and the inner wall of the cage. That way, even if they absolutely destroy the tube, there will be something between the fat end of the bolt and the cage, so there won't be any exposed melamine.
