My rats love to pull the fabric off the shelves to make HUGE nests, so yes, many rats will love to make ugly nests
I usally give mine lots of paper towels, pieces of fabrics, old shirts, toilet paper rolls, tiny cardboard boxes and pretty much everything that isn't harmful and that would anyway go to waste. I even take pieces of fabric and tie them to the sides of the cages so my girl Sake can chew them off and use them as nesting material, it keeps her occupied a lot of time and she seems to love chewing those things and drag them to her nest.