The short answer is "yes". However, based on my own experience, batting simply isn't thick enough nor absorbent enough if you are planning to sew it between layers of fleece for cage liners. Based on many, many members experiences, I think that most of us agree that you are unlikely to find anything else that works as well, is as absorbent, and is as economical as uHaul pads.
What I DO like batting for is in making cozies, cuddle cups, etc. because I find uHaul to be too thick and too difficult to sew in small items other than what I refer to as "throw rugs" (small area pads).
I use both cotton batting and uhaul and I personally find no difference in absobrancy. I use 2 layers of batting and it is more than enough for my 3 piggies. I find it is easier to see with and easier on drying time. So I say go for it.