Yes, that's what the stitch will do. You're right to treat both loops below the "noose" as one stitch. The single loop that is above the noose is the actual stitch, but those two loops below, which is both sides of the stitch from the row below, like to get in the way.
Keeping the outside edges of the knitting neat is a perennial problem. Some people like to work the edge stitches tightly, to try to keep them from getting too loose. Or they just ignore it. Others do this:
Slip the first stitch of every row.
This will give you a "chain" selvage. It looks nice and neat, and is especially great on things like scarves. What it does, is takes that loose stitch, and stretches it up, so that it span two rows. It's only worked once, every two rows, so it's not floppy. And it gives a nice chain look on the edge.