The best I've ever got out of networking was, "Thanks for re-connecting! You should apply for job #41190, since I particularly know that hiring manager is really motivated to hire! Prepare for questions A, B, and maybe C. Happy to do a mock interview. Good luck!" And I got the job, so that's great! But, have realistic expectations. You're not going to bypass the queue and get an offer letter just because you're good friends with one of that company's Senior Software Engineers.
EDIT: Maybe it's different at the ultra-high level, like "VP of Engineering." I have no idea, never been up to that level and don't have peers there. But I can't imagine that a "VP of Engineering" candidate has to do phone screens, and grind at the whiteboard, and have to deal with recruiters and ghosting. Maybe they don't even have to apply and get traditionally interviewed like us commoners. Who knows? Any VPs of Engineering on HN care to chime in and describe how hiring works at your level?