My personal opinion is that based upon the school, the sport, the coach, and the player – the influence can obviously range. That said, a strong word by a coach/faculty is surely going to add value. I believe it has higher value than a teacher’s reference. I know when I am hiring someone the internal reference is more important than the employer’s reference.
I’m always comfortable with “It depends.” 
Just trying to discourage people from reading the tea leaves. Best wishes to all applicants for good news on M10!
Thank you @GoatMama - my kid hasn’t heard a peep from any coach except initial introduction emails when he filed his applications. I was beginning to read between the lines with this also… 
Unsuspecting New User: CC… Help me…This and this happened… blah…blah…blah…WHAT CAN I EXPECT?!"
CC: “Oh dear…Oh my… I am so sorry…My dear…You have the Grim”
My son has been in contact with multiple schools and their lacrosse and football coaches. He has had a lot of communication from the coaches as well as players. Some schools have a coach on the admissions board. Others (Exeter ) have to write a report to admissions for the student. The coaches told me they don’t know who has made it in until M11!
I would not compare your son’s experience with other sports. (That is to say don’t freak out!!
I am very interested to hear how this turns out for the OP’s DD, especially as it relates to the two schools who have contacted her recently. I am also interested about how things turn out for @buuzn03 child where no contact has been made. Only 1 week remaining!
My son went thru this process as an athletic recruit. He was one of the top recruits that year for his sport. Met with all the coaches. All of the TSAO coaches were in radio silence after Feb 1. All except the Hotchkiss coach (who also was on admissions).
The Hotchkiss coach sent friendly emails starting late January to my son. Usually once per week. Nothing in the email mentioned anything about admissions but it was strange to hear from him since no other coaches were saying much. But he ended up getting in everywhere, even those coaches with radio silence.
So bottom line: communication can mean something or it could mean nothing. No way to know until M10.
I’m interested to find out, too @BigBlueSwim. I guess I’ve been thinking that wherever DS actually gets in (hopefully at least one school thinks he is worthy), it is up to him to show the coach that he was worth pursuing. And if there is anything DS does best…it is working hard to prove himself! I’ll be honest, though, in a way, the coaches that didn’t even bother to answer the emails he sent them, I am hoping he is able to avoid. I understand being busy, but just a quick “thanks for your contact” would’ve been nice.
Similarly to @sgopal2 my DS had two coaches reach out to him and two that didn’t after applications were due, but was ultimately accepted at all four schools. The one non TSAO coach was in contact about every other week, asking about how school and training were going. The only TSAO coach who did reach out after the deadline was just letting him know that he was going to be out of the country chaperoning a school trip and would not be immediately available after M10. We took that contact as a good sign, even though he said nothing that was even a hint of you’ve been accepted and even wished him good luck on M10.
@buuzn03 I fully agree that to not reply to an email from a perspective candidate is bad form and would turn most people off. My son was debating about which was going to be his 3rd sport at PA and reached out to one coach multiple times well after being accepted and committing to go there with questions about the program and possible summer camps, but heard nothing back. The coach of the other sport he was looking at did respond with not only a general “great to hear about your interest”, but sent him both information about the team/program as well as recommended summer camps and training plans. Needless to say that made all the difference.
Prospective^
sgopal2 points out something important. There is an agreement between TSAO schools that any contact between coaches and applicants is strongly discouraged (or forbidden) between the application deadline and M10. I know of a few coaches in TSAO schools who have been called in by administrators and “spoken to” for violating the policy, I also know a few coaches who openly violate the policy with no consequence. So, no need to panic over the “radio silence” it just indicates that the TSAO coaches are doing the right thing.
Also, TSAO rules allow coaches to reach out to accepted students ONE time between M10 and April 10. Of course, they can respond to all of the the emails/calls that you initiate. There are coaches who break that rule. Last year I seriously considered reporting one of them for repeated unsolicited phone calls and emails but eventually decided that it’s not worth it. DD didn’t enroll there.
@hola3 that is an important fact I didn’t know. It explains a lot!
Of note, all of my kid’s outreaches were way before the deadline…and most in the “off-season”…many did not show up for his interview, although they had said they would try, but a few have never even acknowledged him at all…those are the ones I was most curious about. On the other hand, there were several that responded, took time to meet him, etc…and even if they were just putting on airs…they took time out of their day, which, as @BigBlueSwim said…makes all the difference. It will be interesting to see how receptive they may be come M10, should he be accepted. Thanks everyone, for your input!!!
TSAO technically cannot recruit. Some attend games that are close by the schools but usually they accept videos and look online for stats. We had two TSAO coaches attend games and communicate afterwards. Much to our surprise. Questions to ask include will you support with admissions.? Will he or she be on varsity? The most difficult question is when they ask if you will come if accepted. Are we your first choice? If you are asking for financial aid you have much more latitude. You can first choice a school but if you get more money elsewhere no one can fault you for that decision.
My son received several calls and contacts from TSAO coaches after the admissions deadline. One even said that he was pushing for a strong freshman team and was hoping that my son would be the anchor. Other coaches didn’t acknowledge my son’s emails - even after specifically asking him to send videos. It will be very interesting to see what happens on M10.
Thanks again for all your responses. Just to update our situation, one of the two coaches I referenced in our OP has emailed again. He is going to be in our area early next week and would like to get together. Just to be clear, the dates he is suggesting to get together are after M10. He didn’t say one way or another in his email, but this coach must think our DD is in, otherwise, why suggest meeting with us right after M10? Also, you could strongly infer from his email that he has seen her application, even though he isn’t in admissions. So maybe the coach/admission contact depends on the school, or even on how active the coach wants to be. Also, this coach is at a competitive New England prep school that gets mentioned on these pages with some frequency, but it isn’t a TSAO member school, so maybe he doesn’t feel bound by all the same rules.
@Hulahoop45 - sounds like it to me, but what do I know? LOL.
Let us know!
Also, anyone know if AO’s from different schools talk to each other? Is there some unwritten rule that they can talk in generalities but not mention names? Or is it totally taboo? Any thoughts or knowledge?