Yes, you iron the fusible on to the wrong side of the t-shirt fabric. You are describing the correct procedure; cut the t-shirt fabric as large as possible, fuse to the wrong side, then cut the fused t-shirt piece down to the correct size.
It's a good idea to experiment on some scrap pieces to be sure you know how hot your iron needs to be and how long to keep it in place. Many fusibles come with this information, but fusible tricot in bulk may not.
T-shirt quilts are usually tied or machine-quilted around the blocks only; you would never want to try to hand quilt through a fusible. Warm 'n' Natural is probably a good batting choice for a t-shirt quilt because it does not require close quilting.
Last time I checked, JoAnn's carried fusible tricot only in small, relatively expensive packages (pre-packaged yardage). It is a lot cheaper to buy it in bulk from a drapery shop. This is where I purchased mine:
http://www.bblackandsons.com/tricot-...-60-p-302.html
If you don't use fusible tricot, be sure to experiment to make sure the fusible you choose is sufficiently light in weight and doesn't make the fabric too stiff. I think you would want to look at only non-woven fusibles for this project.