Could you use balsa wood to hang an heirloom crazy quilt by using fabric glue to glue it on?

I would not recommend using glue on an heirloom quilt. A better solution would be to create a pocket (or sleeve) for a curtain rod to go through, and then sew that to the quilt.

For detailed information on how to do this (with illustrations!), please see the related Quilt Woman link, listed below: