Interference or Not?

[BK47]

Saw this in a travel league game the other night.

Situation: No outs, R1 on third, RHB in the box with 3-2 count.

Play: Batter receives ball four, ball hits the dirt in the LHB's box, catcher moves over to block the ball. As the catcher blocks the ball, the ball bounces forward. Umpire tells Batter its ball four and to take his base. While the batter starts to leave the box, R1 sneaks down third base line as if to steal home, catcher quickly gets the ball and trys to throw down to third however the batter, as he is leaving the box on his way to first, is in his way. R1 goes back to third in the failed attempt to pick him off.

In this case, since the batter was awarded first on ball four, is he protected from batter interference as he was trying to go to first?