I like to do my machine fancy stitches on top of each piece before I set the next one. I use a muslin backing and have found I don't need additional stabilization, but I'm using decorative stitches, not true embroidery.
If you sew all the pieces together first, and then do all your machine embroidery, you'll have to be very careful about starting and stopping if you want to look like something goes underneath the next piece.
I've pieced crazy blocks with foundation and without. I was not planning on doing any decorative stitching on the one without. I have done machine applique, and found I have to use stabilization underneath or I get puckered stitching. If I'm doing a real wide satin stitch, I can still get puckering even with the muslin, unless I go slow and hold the fabric taut while stitching.