Personally, I would do a more traditional quilt as you go process. I would assemble (with backing) the 'body' of the quilt which would be the part that is on the top of the mattress and quilt that. I would then assemble (with backing) and quilt the borders, then attach them with your favorite QAYG technique.
Your method would depend on how sturdy the batting was to survive quilting without a backing. Then the backing is going to be flapping in the wind. I think you would be constantly struggling to keep the backing & quilt together.