To answer your first question, yes, spray starch will stiffen up your fabric so that it doesn't stretch and move while working with it.
Now to answer the question you didn't ask. Even though starch will firm things up, that firmness will disappear when the starch is washed out. You'll be back to the original flimsy fabric in the end. If the quilt will be quilted close enough that your fabric won't have a chance to wobble, etc., you could still get by with that. But, if the rest of your quilt fabrics are good firm ones, the flimsy will probably not wear as well or stay as flat as you'd like in the end.
I've taught lots of quilting classes and I know lots of ladies want to save a buck or two when making their quilts. I always want to save a buck or three!! It really shocks people to see how much fabric, thread, batting costs these days. But I always say, make your quilt with the best you can afford. Why would you spend all that time and money on materials that are sub-par? You want your quilt to last a long time.
Okay, I've probably said too much. But, you did ask!