It is still very early. Many people won't submit until they have their April MCAT scores in June and some will not submit until after they get their August MCAT scores. Other procrastinators won't submit until the winter. I think anytime in June and even July is still very early and a good position to be in so don't worry about beating the crowd on day 1. Many schools wont send out their secondary until mid-July which means anyone who sent the AACOMAS before that will receive their secondary at the same time and be at no advantage.
The trick is to send back the secondary as soon as you get it and have AACOMAS done by mid-July when the secondary start coming out. Good luck