Oriole21 -
Here's how it works. The coach asks for transcripts and test scores. If the coach wants you, he will then make you an offer, you will accept, and THEN he will ask you to fax or mail an application to him complete with application essay and fee, etc. He will then walk it through the admissions office. You are not "officially" admitted until you get the letter from the admissions office. For Spring offers, this could come long after everyone else has already received admissions letters.
As to your second question, on an earlier thread (which you will have to find), a parent stated his son was admitted to a school to play baseball, even though he had been initially rejected.