runner hit by ball - what about the batter?

[myczek]

Here's the situation: Runner in first with 2 outs. The batter hits a ground ball between first and second and the ball hits the runner (before passing a fielder). The runner is called out for the 3rd out.

My question is what is scored for the batter? Is he given an at bat and it is scored like a fielders choice? Or does it not count as an at bat? Or something else?

Also, would it be scored differently is it was not the 3rd out of the inning?