Or is it just the final clutch at an ephemeral straw?
Effective at what?
Are you asking if people get in after deferrals? Yes. How many? Different at different schools.
I mean, does sending a letter to admissions improve your chances? CommonDataSets tell you the numbers.
If a school had one spot left, and two otherwise equal applicants (unlikely), a letter might make a difference.
A Deferral is viewed just like any other RD - maybe they wanted to see Senior grades, but it’s more likely they liked what they saw enough to take another look as compared to the rest of the RD applicants. An expression of interest is good to send, but as @vonlost stated it is best a tie breaker.
Breaking a tie is meaningful if you’re the guy who didn’t write the letter!
There is no empirical evidence that I know of to prove that a letter of continuing interest will make a difference in an admissions decision. Even if there was evidence, no one answer will be correct for every college and every admissions officer.
That said, let’s go with common sense. If an applicant has any new significant accomplishments since the application was submitted it can’t hurt to let admissions know. Or if an applicant confirms interest in the school (and can honestly say “if accepted I will attend”) again, it can’t hurt. No admission officer wants another long essay to read but it seems to me that one succinct update (especially if there is something new to say) isn’t a bad idea.
Unless you make it really annoying (e.g. weekly e-mail), sending in LOCI would not hurt at all. It may give you a slightly benefit. It may be more crucial for waitlisted students.
A deferral at different schools, can mean different things. At a Stanford for example, they defer very few at EA, so a deferral means more there than at say Yale, where they defer about 60% of EA applicants. G’town defers most at EA too. So you really need to investigate how your school handles deferrals. In many cases, it equals a polite deny, but not always.