What if someone could run so fast they could do this?

That is scientifically impossible. The body could simply not withstand it. About running from west to east coast, would be impossible too, because its not that he is moving faster, its that time is moving slower for him. He would run as far as his physical capabilities would allow, becoming tired. He would just experience it at extremely high speeds. Another reason this opinion would fail is because the particles in the air(oxygen, hydrogen, etc) wouldn't move fast enough to support the lungs. The only way this would be possible is if he could control when he stops, which would cancel out every thing I just explained.