You can make a quilt out of cross-stitch pieces. There was a discussion on a longarm group about how to quilt something like this. I thought you would need to go around the cross-stitching, but some posted that they had done overall quilting on cross-stitch quilts and they came out beautifully.
This may be a quilt that you would want to dry clean, as there is no way you can be certain that all of the embroidery threads used are colorfast. I think that older threads are colorfast but some of the newer ones are not because of the banning of some of the chemicals used in the past. Also, the base fabrics for the embroidery may shrink at different rates. This is not as much of an issue with close quilting lines, but could cause distortion if quilting lines are further apart.