No, it's a bit smarter than that. Try the following experiment. On a treadmill, start running at a slow pace. Run naturally, avoid raising your arm to look at the watch. Run for some time, just to allow the measured pace to settle at a stable value. Then, after a minute or so, exagerate your arm swing without increasing cadence. You'll see an increase in indicated pace. So it's not just cadence multiplied by average stride length.
