I think it would make a beautiful backing. I'd try it on one and see how you like it. I got this curtain material at a auction and it has this beautiful Japanese print on it. The fabric is vintage and it washes up very nice. I am going to us this fabric in a quilt. Sometimes thinking outside of the traditional way of doing something can end up being something quite special.

I have used a 4th of July tablecloth that was not being used and it was a thick fabric...just quilted around the blocks on the whole cloth and did a backing of similar fabric. It came out great. Used a larger needle for the quilting 90/14 and a 50 weight cotton thread

Once you have quilted a quilt with linen on the back, wrinkles become a non-issue. You have texture, which is what I like about quilts anyway. I have used 100% linen, and most recently a linen cotton blend. Of course, an older linen item has probably been washed many times - but I recommend that you wash and dry "new" fabric several times as shrinkage is definitely a factor.

Now I am sorry that I donated all of my linen and damask cloths to a thrift store.