Mine was quilted block by block rather than "As you piece". Each block is a little quilt, really. I did use basting spray on each block to hold it together while I quilted it so I wouldn't have pins in my way.
I believe you could leave a little extra batting around the edges of each block and zig-zag the batting back together, then cover with single thickness sashing strips if you wanted to. The lady I saw doing it this way used single thickness sashing on the front and double on the back and then hand stitched the folded edge on the back side just like binding.