https://goo.gl/photos/bxFJsJMUvj6hT6as8No I quilt right to the edge of the pieces.
You can QAYG in multiple blocks, Quarters, thirds or halves.
Ruebens treasure Map quilt was quilted in (I think) 12 blocks
The HSTathon was quilted in thirds
and Lucias Black and White jobby will be quilted in halves.
All of these have visual allowance for the joining strips.
I have never QAYG'ed without them I'm afraid but understand the basic premise ...
Leave an inch unquilted on either edge of the pieces you want to join.
Trim the batting to 1/4" less than the top on either side
Right sides together of the top and stitch ... and I have no idea how you stitch the bottom closed.
I do have the Ann Peterson (?) Craftsy class on Quilting Big Quilts on small machines, I could further investigate if you wished.
The mystery quilt can only be QAYG'ed if you add borders...Which I did with the one I gave my Auntie Gell, but the centre has to be quilted as a whole ...which it can as I did it!