Do HS counselor relationships with ivy leagues help for waitlists?

I was waitlisted at Cornell and my HS counselor said she would be able to call the AO to advocate for me. She didn’t disclose the specific details of the conversation besides the fact that I am very interested (something like that haha she was very vague). Is it true that attending a hs with a pretty strong relationship with a college puts you at an advantage in getting off the WL? I go to a private school that sends a handful of kids to ivy leagues each year, especially Cornell, and I’ve been told that our school has high success in getting kids off these WLs. I’m still learning how the waitlist works but I also don’t want to get my hopes up since she told me that an advocacy call from her might be of help.

(I genuinely feel like I’m spiraling into this realm of pretentious private school kids but Cornell is genuinely my last hope😭)