I have washed a piece of "naked" warm and natural batting twice - and it looked fine after the washings.
You could take a small piece of it and wash it several times and see what it does. I don't think it is designed for a lot of abrasion like the outer fabrics of a quilt frequently get - but I dont' know the answer.
You could also baste a small piece of it on to a quilt or blanket that you use frequently and see what happens.
Bottom line - I really don't know the answer to your question.