Sometimes it also works for the Public Ivies and competitive state universities.
Our DS (AFROTC) did not apply to UNCCH or NYU Sterns (both OOS), however, he was offered admission to both colleges. When we got the congrats letter I was stunned and floored. I thought that this had to be a scheme and somehow they were looking for money. DS didn't want to attend either school, but curiosity got me going. I called both schools admissions and offer and they stated that yes he was admitted, and yes they knew he didn't apply.
~ The AFROTC CoCs sat on the admissions board and so when the list was released from the scholarship board they saw that he was a match and they offered him admissions.
That being said, Coolcats please take note the key word is MATCH. If you are applying only for reaches than don't assume that it will help. I doubt that if you have a 32 ACT superscore with no strong ECs that you will get an edge just for receiving a ROTC scholarship. However, typically if you are a ROTC scholarship recipient you typically will also see nice merit packages. Our DS had merit packages up to 100K.
As for Notre Dame that was the 1 school he was waitlisted. He had a 34 best sitting and a 1390 best sitting SAT. He was a National Merit Finalist. Top 7% of his class. All APs (I think 9 by the time he was a Senior in HS and did jump start too. His uw cgpa was 3.86. 2 time state champion for Tae Kwon Do. Junior Olympian Bronze medalist. Senior lifeguard with 23 saves. Basically, he wasn't just academics and still no offer of admissions.
Finally, something to realize regarding ROTC scholarships, many SA candidates will also apply for ROTC scholarship as plan B. They will be your competition.