Will skipping a seam (attaching two pattern pieces) on a shirt change how the garment hangs?

As long as it doesn't change the grainline of the fabric pieces, it will not change the hang. It will look kinda funny without a seam that's meant to be there.

Take a look at one-seam pants compared to the usual:

http://www.dprakash.net/sewing/knot_capris.html

More on kimono:

http://www.costumes.org/shows/100pages/MIKADO3.HTM

Having made some things by draping (folding the fabric instead of seaming) you might get away with it for a really soft fabric, but with more ordinary fabrics, the slope of your shoulders and the taper of your body will not be matched by simply wrapping the fabric without seams - the seams add material in the wider parts and remove in it the narrow. A folded fabric over the shoulder will either bind near the neck or stand up over the point of the shoulder looking awkward.

Since the top and bottom are the seamed parts, then that seam goes around the middle horizontally. I can't visualize how you can attach two pieces and have a shirt, but if the wraps attach at the middle of the back, then the shirt won't really 'hang' because it will be tight around the torso.