Crossed Signals

The following situation took place in the Belmont/Dracut State tournament game:

Runners on 1st and 3rd. 1 out. The steal sign is given to the runner on 1st base. The runner on 3rd base mistakenly takes off for home, thinking the steal sign was intended for him. The pitcher steps off the mound, throws to the catcher, and the runner is thrown out at the plate.

Question: If the batter had thrown his bat at the ball and made contact, what would the call have been? It's clearly interference on the batter, given that it was not a pitch. Is the batter called out and the runner sent back to third? If this is the case, it would have been the best move for the batter if he believed the runner would be out at the plate. 1st and 3rd with 2 outs beats having a runner on 1st with 2 outs.