I used to see this guy when I was out running who really swung his arms crazy. He mostly swung one more than the other though. I always thought, "That guy needs to work on his form." Then once, when he passed me in the opposite direction, I could hear him counting his cadence under his breath. Ha!
Oh, definitely. You want your arms to swing forward and back, in the same direction you intend to go, forward. We don't want to go sideways. Swinging our arms sideways wastes energy and slows us down.