throwing bat at ball

[scyguy]

Atl, if the batter makes contact with the ball when his foot is outside the box or on the plate, we have a dead ball, batter out. If R3 is stealing home, we have to send him back to third.

If batter throws bat at ball and makes contact and his foot was outside or in contact with plate when bat LEFT HIS HAND, then we have a dead ball out on batter, runner back to third.

Does the above action supercede calling batter interference? I guess what I am asking is, for the above infraction, will we call out the batter or the runner if we have less than 2 outs.