When S went through the process, his school only offered RD (it has since changed to offer EA also). But he was also recruited by schools which had ED/EA options. Those schools told him that often they recruited all the way through March if their supply of LLs hadn't been exhausted.
Theoretically, admissions runs the show for athletic recruits in the Ivy. That having been said, once a coach has been at a school long enough, he has a great feel for the academic bar needed to get most recruits admitted (the general exception is the future Ivy League POY who has a 28 ACT.) (If the coach is new, his feel for the admissions standards may not be that developed.)
For athletes, the coach makes a non-binding offer, which the player acts on by submitting a completed application. Special committees review the applications (because the kids need to know if they will be admitted and won't stop their recruiting efforts until assured of a spot) basically when submitted and if admission is granted, the Likley Letter is then mailed. The LL is a guarantee of a spot in the class (subject to character issues, etc,. just like all other accepted applicants) which is then confirmed with the formal acceptance (around April).
One item which distinguishes the Ivy schools from other D1s is the limited number of recruited players a coach can secure each year (even if there is technically room on the roster). That limit is expressed by the LLs the coach is allocated (usually 6 -8, though apparently Penn has at least temporarily found a way around that). A coach will not commit to a LL unless he is sure the kid will accept (yes, occasionally a kid will get an LL and not accept but that is a rare case and shows the coach didn't do his homework; a part of that homework is determining if a kids family can pony up with whatever is needed to fill the FA gap).
So, it works something like this: coach has a LL available, coach ranks the players available based upon ability and admissibility, coach works down the list determining who will accept an LL. The acceptance of the LL from the family's side will often depend upon finances and the coach needs to close that loop. If the coach is wrong about the kid accepting the LL, the coach not only loses that player, but doesn't get to get an LL for the next kid on the list. In that case, coach has to hope that latter kid can get through admissions without athletic support (e.g., alum, developmental case, national spelling bee winner, etc.). If a kid doesn't get an LL, theoretically he competes with all other applicants.
FA is a non factor for admissions; but FA may be a factor for the family. Coach needs to know whether his last LL will be wasted on a kid who can't afford to attend (or whose family can't suffer the financial pain).
As further unsolicited advice, I'd have the kid submit an application even without coaches support (unless he's committed to another D1). But the application must be treated as if he were a regular student. In other words, great essays (S's were pretty mediocre), overwhelming EC's, LORs, and the rest - the best application the kid can do (kids whose applications go before the special athletic committees don't need to have that type of application). He has nothing to lose but time and effort.