1) they will get it automatically
2) schools may or may not automatically update their system nor can be assured an evaluator will see it before moving you to adcom review
3) Any email you send requesting the school look at this letter or the simple act of having the letter assigned in AMCAS implies that you are requesting your file be removed from completed status, have the letter added, and now put back perhaps at the bottom of the queue. Therefore your application will be considered complete the date the letter is added.