Yep. It's why so many important races end up suspiciously razor-thin close. A statistical impossibility for that to happen so frequently, but there it is.
And to piggy back on your thought, the law of averages tells us that at least once, these suddenly found votes would be of advantage to the GOP candidate. Yet it is always the Dem candidate that comes from behind to win.
Another reason public schools have been slowly getting worse in the last 60 years. Politicians have a vested interest in citizens that can’t think things out, do simple math, or use logic.