That would be a dumb thing to do. Don't know if it changes medical status but it will have to be approved if you've gotten it and it could be remove it or bye-bye afterwards.
This issue seems to come every year and I just can't figure out for the life of me why you can't wait ? If you want the tatoo at 18 prior to going in to USNA< USMA, USAFA or ROTC won't you want the tatoo after you graduate?
Don't risk your appointment/scholarship for something like a tatoo