Every rifle bullet wobbles a little when it leaves the muzzle, but if the rifling twist is enough for the bullet it quits wobbling very quickly. That's what's meant by the bullet "going to sleep."
However, the average shooter apparently believes the wobble is much greater than it actually is. Unless the twist is totally inadequate for stabilizing the bullet, firing a shot at a target 10 feet away results in a round hole of bullet diameter, not an oblong.
There is some VERY slight effect on ballistic coefficient due to bullet wobble (or "precession") from the muzzle, but not enough to show up even at several hundred yards, as long as the rifling twist is sufficient to really stabilize the bullet.
