JacquiGates

I have made 27 dresden plate squares. I want to make them look old fashioned and want to do blanket stitch around them. Question is, do I do the stitching (by hand) with the batting and backing on or do I do it just on the blocks. I am going to do a simple stipple on the outer part (doing quilt as you go). I have been stuck on this for over a week and need to get moving on it..
Thanks for any help