Yes, it can be done! In my opinion it is a way of preserving something that would otherwise be stuck in a drawer. A quilt would be lovely.
I am presently working on the same idea. I have a tablecloth made for me by an 89 year old, now deceased, lady, but it does not fit our dining table that well. I am putting borders around it (stitching it down by applique) and then will quilt the whole thing with a special design in the middle.
My tablecloth is also a blend so the fabric used on the borders will be pre-shrunk or also a blend (same with batting and backing). The back will have a label with her picture, dates, etc.
Cindy Needham has a book out about Wholecloth Linen Quilts that you might find interesting.
Good luck.