Yes and no, Stanford has several players who committed (last year 3) who have had to decommit when they got the skinny envelope from admissions. Last year the teams earliest commit (committed 18mo before LOI day), had to re-open his recruitment due to admissions. He ended up committing to Vandy or Wisc IIRC. Several soft commits according to members of the alum and team I converse with have not openly committed until they knew their admission status. This year there are at least 3 silent commits, I cannot discuss who, who will know where they are going after letters from admissions come out.Because of their academics though, they are already at a disadvantage because there are players they can't even talk to because of academics.
@SUBuddha can correct me if I'm wrong, but I believe they typically have 3-4 every single year actually sign LOI's who actually look good, but still end up not qualifying. Add to that the fact that most of Stanford's players stay 4 years and top level recruits, in general, are only looking to play 3 years and it narrows their pool of players even more.
The best thing a recruit who has the test scores and required 3 AP classes both Jr and Sr. year can do is apply for selective early admissions. If they get denied there they can re apply with new GPA and test scores later. The real issue is simply this, there are a lot of kids who would like to go there, and even with sliding admissions scoring based on combined test scores/GPA, letters of Rec/essays and extra curricular activities means more stars reduce GPa or grade limits, but not by much. However, the university sets their incoming class size on many factors, among them is available housing (all frosh are required to live on campus and be part of random roommate assignment, no jock dorms). If the recruit does not make preferred admit status they are competing against 30-40k others for about 1100 slots. Keep in mind the average Stanford freshman class is 1400-1700 students. The regular admit students get their letters in late January. Early admission applicants have received their letters already or will in the next few days.
To put this in perspective, of the 20 verbals Stanford has this year only 6 have received the fat envelope from early admissions applications. Three preferred walk on's also go letters today (if Twittter is to be believed). Scuttlebutt is the staff could lose 3 or more of scholarship commits and at least 2 silent commits if the latest SAT and ACT scores are not favorable.
To your other point, even with early exits (Peat etc.) the team has a 99% grad rate. So yes most players, even if they only stay 4 and not 5, do stick around. The benefit of red shirting and staying a full 5 years is that about 60% of Stanford degrees offer a Co-Term or accelerated 1 year masters program. So staying for five (if the kid red shirts) can allow them to have a BA/BS and MA/MS from Stanford even if they never sniff the field for an NFL team. That is a heck of an earning boost over many schools elsewhere, just based on degree name.