ASA 5-8-A-Note-B

"A home run will be charged for any ball hit over the fence whether runs score or not."

If a batter hits a ball over the fence and is called out on appeal for missing a base, a home run is still charged toward the team's limit. (Obvious exceptions are divisions that do not require the runner to run the bases.)

Am I right that this also applies if the batter is called out immediately for having a foot out of the box and making contact?

No. If the foot is out of the box, the ball is dead immediately. It is never fair or foul, is never caught or uncaught and is never over the fence for a "home run".

The penalty for making contact with a pitch while out of the box an immediate dead ball and the batter is out (POE 7). Since it's an immediate dead ball, I can't see how they could count it as a homerun.

This happened last night, and we did not count it against the total. It made a difference, too, as both teams exceeded their limit (of 4).

At first, the idea of counting the out against the HR total didn't even enter my head. But a couple of innings later, I thought about it, and my first reaction was that because the batter was immediately out, he technically didn't hit a ball over the fence. In fact, he technically didn't hit anything.

But I wasn't sure, and when I looked it up last night, I still wasn't sure.

A recent ASA test had a question about a batter who, with a runner on 3B, hit a fly to left and threw the bat in anger, only to have the ball go over the fence. The correct ruling was immediate ejection for USC, out, and the runner goes back to 3B.

Should that play count against the team's HR total?

While you didn't state it, it sounds like a Dead ball out for the USC. Since the runner went back to 3rd, there is no benefit from the play, so it must have been a dead ball. In this case, I think I would count the HR, as far as the totals go, but not in the case in the origninal post.