In med school admissions, I'd say "not helping" is the same as "hurting" due to the level of competition.
That being said, someone with literally NO leadership experience (of any kind) by the time s/he graduates college doesn't have much chance in any career (considering that most college graduate entry-level positions have a track into some sort of role that either starts with or progresses into leading/supervising other people, to include sitting on committees that make decisions or recommendations to the organization). OP, I am sure you have had some sort of leadership experience (talking situational leadership here -- not necessarily positional leadership). I'd suggest you find opportunities to lead people and get that experience if you haven't already had it. Keep in mind that TA'ing can easily become a leadership experience (start leading study groups, etc., or working with your prof to find other ways to lead). Go get a part-time job. That could offer some opportunities (esp. if you can snag a shift lead or mgmt position).