Wow, I'm not sure. Are the fabrics delicate? Do the stitches seem delicate?
I'm by no means an expert in this, but I would think the original quilter meant for it to be finished one way or another. I would definately put a backing on it and maybe hand quilt it, if you're really worried about putting the fabric through a machine to quilt it. Or else, maybe you could tie the quilt instead of quilting it, but from the back of the quilt, that way you don't have little bits of yarn or floss distracting from the work on the front of the quilt.
Can you show us a picture? I'm sure other people will come along with more ideas or suggestions for you :)