I see no reason you can't do that. I have a quilting friend who does it all the time - but she limits herself to 9-patches made from the 1" squares, and then sets them with 1.5" (finished) alternate blocks of a solid fabric.
When you sew the seams, you need to be very careful of your seam allowance. And in order for the second pass (sewing the other direction, across the first lines of stitching) to lie nicely, you should clip the seam allowance of the fusible at each intersection, so you can press each row in opposite directions and nest the seams.
Edit to add:
I guess I didn't read far enough before posting. Those blocks look great!