What question is the OP asking, exactly?
If you're asking whether you tried out for moot court, and went up the semi-final round of tryouts, etc, but didn't get a place on the team, can you put that you participated? That answer would probably be no. That's like saying, "I competed in the Law Review write on, but didn't make it." and putting it on your resume.
If you were invited in the Moot Court Society/Team, then it can definitely goes on the resume whether you win competitions or not.