If the runner is attempting to touch home plate, I would not call the runner out for incidental contact by his teammates. However, if they would, for example, carry him off the field and he never attempts to touch home plate, I would call him out when he reaches the dugout area.
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If the defensive team properly appeals that the batter missed touching second base, he is called out on appeal, and his run does not count. However, any other runners on base at the time of the home run would score.
If the Home Plate Umpire rules that the batter did not attempt to avoid being hit, batter does not get the pass to first base.