My son had a mediocre AIME score (3), got into Harvard and CMU, deferred and then rejected at Caltech and MIT. Waitlisted at Harvey Mudd. Quite a while ago. I assume it was slightly in the plus column, but really just confirmed he was more interest in CS than math. He never studied for any of those math competitions.
I don’t think of taking the AIME as an EC in and of itself. It’s just an award you can list.