You could certainly do part of the quilting using only the front and the batting. I do that when I'm putting raw edge applique on a quilt. BUT you must all do quilting on all three layers: front, batting and back and make sure the quilting lines meet the criteria (e.g. 5 inches between quilting lines) your batting calls for.
I will do difficult quilting or quilting with metallic thread on just the top and batting and add easier quilting to all. three layers.[ATTACH=CONFIG]565727[/ATTACH]In this quilt I did the letters and the animals without the back on and then I added the back and did the quilting that matched the yellow front and back. That way my back didn't have all the different colors on it. I prefer if the quilting doesn't show so much on the back. Also it is actually easier to do this fussy raw edge applique quilting with just two layers instead of three. Hope that helps.